diff --git a/packages/@ourworldindata/core-table/src/CoreTableColumns.ts b/packages/@ourworldindata/core-table/src/CoreTableColumns.ts
index 390dfb88bc..64b355d867 100644
--- a/packages/@ourworldindata/core-table/src/CoreTableColumns.ts
+++ b/packages/@ourworldindata/core-table/src/CoreTableColumns.ts
@@ -536,14 +536,16 @@ export abstract class AbstractCoreColumn<JS_TYPE extends PrimitiveType> {
     // assumes table is sorted by time
     @imemo get owidRows(): OwidVariableRow<JS_TYPE>[] {
         const entities = this.allEntityNames
-        const times = this.originalTimes
+        const times = this.allTimes
         const values = this.values
+        const originalTimes = this.originalTimes
         const originalValues = this.originalValues
-        return range(0, times.length).map((index) => {
+        return range(0, originalTimes.length).map((index) => {
             return omitUndefinedValues({
                 entityName: entities[index],
                 time: times[index],
                 value: values[index],
+                originalTime: originalTimes[index],
                 originalValue: originalValues[index],
             })
         })
@@ -562,6 +564,23 @@ export abstract class AbstractCoreColumn<JS_TYPE extends PrimitiveType> {
         return map
     }
 
+    // todo: remove? Should not be on CoreTable
+    @imemo get owidRowByEntityNameAndTime(): Map<
+        EntityName,
+        Map<Time, OwidVariableRow<JS_TYPE>>
+    > {
+        const valueByEntityNameAndTime = new Map<
+            EntityName,
+            Map<Time, OwidVariableRow<JS_TYPE>>
+        >()
+        this.owidRows.forEach((row) => {
+            if (!valueByEntityNameAndTime.has(row.entityName))
+                valueByEntityNameAndTime.set(row.entityName, new Map())
+            valueByEntityNameAndTime.get(row.entityName)!.set(row.time, row)
+        })
+        return valueByEntityNameAndTime
+    }
+
     // todo: remove? Should not be on CoreTable
     // NOTE: this uses the original times, so any tolerance is effectively unapplied.
     @imemo get valueByEntityNameAndOriginalTime(): Map<
@@ -577,7 +596,7 @@ export abstract class AbstractCoreColumn<JS_TYPE extends PrimitiveType> {
                 valueByEntityNameAndTime.set(row.entityName, new Map())
             valueByEntityNameAndTime
                 .get(row.entityName)!
-                .set(row.time, row.value)
+                .set(row.originalTime, row.value)
         })
         return valueByEntityNameAndTime
     }
diff --git a/packages/@ourworldindata/core-table/src/OwidTable.test.ts b/packages/@ourworldindata/core-table/src/OwidTable.test.ts
index a58250a1ec..3220831096 100755
--- a/packages/@ourworldindata/core-table/src/OwidTable.test.ts
+++ b/packages/@ourworldindata/core-table/src/OwidTable.test.ts
@@ -72,7 +72,7 @@ it("can parse data to Javascript data structures", () => {
     table.get("Population").owidRows.forEach((row) => {
         expect(typeof row.entityName).toBe("string")
         expect(row.value).toBeGreaterThan(100)
-        expect(row.time).toBeGreaterThan(1999)
+        expect(row.originalTime).toBeGreaterThan(1999)
     })
 })
 
@@ -632,7 +632,7 @@ describe("tolerance", () => {
     })
 })
 
-it("assigns originalTime as 'time' in owidRows", () => {
+it("assigns originalTime as 'originalTime' in owidRows", () => {
     const csv = `gdp,year,entityName,entityId,entityCode
 1000,2019,USA,,
 1001,2020,UK,,`
@@ -642,7 +642,7 @@ it("assigns originalTime as 'time' in owidRows", () => {
         expect.not.arrayContaining([
             expect.objectContaining({
                 entityName: "USA",
-                time: 2020,
+                originalTime: 2020,
                 value: 1000,
             }),
         ])
@@ -651,7 +651,7 @@ it("assigns originalTime as 'time' in owidRows", () => {
         expect.not.arrayContaining([
             expect.objectContaining({
                 entityName: "UK",
-                time: 2019,
+                originalTime: 2019,
                 value: 1001,
             }),
         ])
diff --git a/packages/@ourworldindata/grapher/src/core/Grapher.tsx b/packages/@ourworldindata/grapher/src/core/Grapher.tsx
index 673b56b316..e85e5f2107 100644
--- a/packages/@ourworldindata/grapher/src/core/Grapher.tsx
+++ b/packages/@ourworldindata/grapher/src/core/Grapher.tsx
@@ -884,7 +884,10 @@ export class Grapher
             )
 
         if (this.isOnSlopeChartTab)
-            return table.filterByTargetTimes([startTime, endTime])
+            return table.filterByTargetTimes(
+                [startTime, endTime],
+                table.get(this.yColumnSlugs[0]).tolerance
+            )
 
         return table.filterByTimeRange(startTime, endTime)
     }
diff --git a/packages/@ourworldindata/grapher/src/entitySelector/EntitySelector.tsx b/packages/@ourworldindata/grapher/src/entitySelector/EntitySelector.tsx
index ebce9d9205..a6590dcf0b 100644
--- a/packages/@ourworldindata/grapher/src/entitySelector/EntitySelector.tsx
+++ b/packages/@ourworldindata/grapher/src/entitySelector/EntitySelector.tsx
@@ -453,7 +453,7 @@ export class EntitySelector extends React.Component<{
                 const rows = column.owidRowsByEntityName.get(entityName) ?? []
                 searchableEntity[column.slug] = maxBy(
                     rows,
-                    (row) => row.time
+                    (row) => row.originalTime
                 )?.value
             }
 
diff --git a/packages/@ourworldindata/grapher/src/mapCharts/MapChart.tsx b/packages/@ourworldindata/grapher/src/mapCharts/MapChart.tsx
index f641a1b939..a07da5438f 100644
--- a/packages/@ourworldindata/grapher/src/mapCharts/MapChart.tsx
+++ b/packages/@ourworldindata/grapher/src/mapCharts/MapChart.tsx
@@ -346,12 +346,12 @@ export class MapChart
 
         return mapColumn.owidRows
             .map((row) => {
-                const { entityName, value, time } = row
+                const { entityName, value, originalTime } = row
                 const color = this.colorScale.getColor(value) || "red" // todo: color fix
                 if (!color) return undefined
                 return {
                     seriesName: entityName,
-                    time,
+                    time: originalTime,
                     value,
                     isSelected: selectionArray.selectedSet.has(entityName),
                     color,
diff --git a/packages/@ourworldindata/grapher/src/mapCharts/MapSparkline.tsx b/packages/@ourworldindata/grapher/src/mapCharts/MapSparkline.tsx
index 7fa2a61dbf..72977920cd 100644
--- a/packages/@ourworldindata/grapher/src/mapCharts/MapSparkline.tsx
+++ b/packages/@ourworldindata/grapher/src/mapCharts/MapSparkline.tsx
@@ -118,7 +118,7 @@ export class MapSparkline extends React.Component<{
             lineStrokeWidth: 2,
             entityYearHighlight: {
                 entityName: this.manager.entityName,
-                year: this.manager.datum?.time,
+                year: this.manager.datum?.originalTime,
             },
             yAxisConfig: {
                 hideAxis: true,
diff --git a/packages/@ourworldindata/grapher/src/mapCharts/MapTooltip.tsx b/packages/@ourworldindata/grapher/src/mapCharts/MapTooltip.tsx
index e58b90c548..65775d51db 100644
--- a/packages/@ourworldindata/grapher/src/mapCharts/MapTooltip.tsx
+++ b/packages/@ourworldindata/grapher/src/mapCharts/MapTooltip.tsx
@@ -119,8 +119,8 @@ export class MapTooltip
             : targetTime?.toString()
         const displayDatumTime =
             timeColumn && datum
-                ? timeColumn.formatValue(datum?.time)
-                : (datum?.time.toString() ?? "")
+                ? timeColumn.formatValue(datum?.originalTime)
+                : (datum?.originalTime.toString() ?? "")
         const valueColor: string | undefined = darkenColorForHighContrastText(
             lineColorScale?.getColor(datum?.value) ?? "#333"
         )
@@ -143,7 +143,7 @@ export class MapTooltip
         const yColumn = this.mapTable.get(this.mapColumnSlug)
 
         const targetNotice =
-            datum && datum.time !== targetTime ? displayTime : undefined
+            datum && datum.originalTime !== targetTime ? displayTime : undefined
         const toleranceNotice = targetNotice
             ? {
                   icon: TooltipFooterIcon.notice,
diff --git a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.test.ts b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.test.ts
index bdfb7d1885..8fdabb7dd4 100755
--- a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.test.ts
+++ b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.test.ts
@@ -49,7 +49,8 @@ it("filters non-numeric values", () => {
     expect(chart.series.length).toEqual(1)
     expect(
         chart.series.every(
-            (series) => isNumber(series.startValue) && isNumber(series.endValue)
+            (series) =>
+                isNumber(series.start.value) && isNumber(series.end.value)
         )
     ).toBeTruthy()
 })
diff --git a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.tsx b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.tsx
index 8e928278f0..4f2130bf8d 100644
--- a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.tsx
+++ b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChart.tsx
@@ -60,6 +60,7 @@ import { ColorSchemes } from "../color/ColorSchemes"
 import { LineLabelSeries, LineLegend } from "../lineLegend/LineLegend"
 import {
     makeTooltipRoundingNotice,
+    makeTooltipToleranceNotice,
     Tooltip,
     TooltipState,
     TooltipValueRange,
@@ -114,12 +115,20 @@ export class SlopeChart
         if (this.isLogScale)
             table = table.replaceNonPositiveCellsForLogScale(this.yColumnSlugs)
 
+        this.yColumnSlugs.forEach((slug) => {
+            table = table.interpolateColumnWithTolerance(slug)
+        })
+
         return table
     }
 
     transformTableForSelection(table: OwidTable): OwidTable {
         table = table.replaceNonNumericCellsWithErrorValues(this.yColumnSlugs)
 
+        this.yColumnSlugs.forEach((slug) => {
+            table = table.interpolateColumnWithTolerance(slug)
+        })
+
         // if time selection is disabled, then filter all entities that
         // don't have data for the current time period
         if (!this.manager.hasTimeline && this.startTime !== this.endTime) {
@@ -276,10 +285,9 @@ export class SlopeChart
             canSelectMultipleEntities,
         })
 
-        const valueByTime =
-            column.valueByEntityNameAndOriginalTime.get(entityName)
-        const startValue = valueByTime?.get(startTime)
-        const endValue = valueByTime?.get(endTime)
+        const owidRowByTime = column.owidRowByEntityNameAndTime.get(entityName)
+        const start = owidRowByTime?.get(startTime)
+        const end = owidRowByTime?.get(endTime)
 
         const colorKey = getColorKey({
             entityName,
@@ -299,8 +307,8 @@ export class SlopeChart
             seriesName,
             entityName,
             color,
-            startValue,
-            endValue,
+            start,
+            end,
             annotation,
         }
     }
@@ -308,7 +316,29 @@ export class SlopeChart
     private isSeriesValid(
         series: RawSlopeChartSeries
     ): series is SlopeChartSeries {
-        return series.startValue !== undefined && series.endValue !== undefined
+        const {
+            start,
+            end,
+            column: { tolerance },
+        } = series
+
+        // if the start or end value is missing, we can't draw the slope
+        if (start?.value === undefined || end?.value === undefined) return false
+
+        // sanity check (might happen if tolerance is enabled)
+        if (start.originalTime >= end.originalTime) return false
+
+        const isToleranceAppliedToStartValue =
+            start.originalTime !== this.startTime
+        const isToleranceAppliedToEndValue = end.originalTime !== this.endTime
+
+        // if tolerance has been applied to one of the values, then we require
+        // a minimal distance between the original times
+        if (isToleranceAppliedToStartValue || isToleranceAppliedToEndValue) {
+            return end.originalTime - start.originalTime >= tolerance
+        }
+
+        return true
     }
 
     // Usually we drop rows with missing data in the transformTable function.
@@ -370,8 +400,8 @@ export class SlopeChart
         const { yAxis, startX, endX } = this
 
         return this.series.map((series) => {
-            const startY = yAxis.place(series.startValue)
-            const endY = yAxis.place(series.endValue)
+            const startY = yAxis.place(series.start.value)
+            const endY = yAxis.place(series.end.value)
 
             const startPoint = new PointVector(startX, startY)
             const endPoint = new PointVector(endX, endY)
@@ -406,8 +436,8 @@ export class SlopeChart
 
     @computed get allYValues(): number[] {
         return this.series.flatMap((series) => [
-            series.startValue,
-            series.endValue,
+            series.start.value,
+            series.end.value,
         ])
     }
 
@@ -522,13 +552,13 @@ export class SlopeChart
     // used in LineLegend
     @computed get labelSeries(): LineLabelSeries[] {
         return this.series.map((series) => {
-            const { seriesName, color, endValue, annotation } = series
+            const { seriesName, color, end, annotation } = series
             return {
                 color,
                 seriesName,
                 label: seriesName,
                 annotation,
-                yValue: endValue,
+                yValue: end.value,
             }
         })
     }
@@ -660,17 +690,37 @@ export class SlopeChart
         const { series } = target || {}
         if (!series) return
 
-        const title = isRelativeMode
-            ? `${series.seriesName}, ${formatColumn.formatTime(endTime)}`
-            : series.seriesName
+        const formatTime = (time: Time) => formatColumn.formatTime(time)
 
-        const timeRange = [startTime, endTime]
-            .map((t) => formatColumn.formatTime(t))
-            .join(" to ")
+        const actualStartTime = series.start.originalTime
+        const actualEndTime = series.end.originalTime
+        const timeRange = `${formatTime(actualStartTime)} to ${formatTime(actualEndTime)}`
         const timeLabel = isRelativeMode
-            ? `% change since ${formatColumn.formatTime(startTime)}`
+            ? `% change between ${formatColumn.formatTime(actualStartTime)} and ${formatColumn.formatTime(actualEndTime)}`
             : timeRange
 
+        const constructTargetYearForToleranceNotice = () => {
+            const isStartValueOriginal = series.start.originalTime === startTime
+            const isEndValueOriginal = series.end.originalTime === endTime
+
+            if (!isStartValueOriginal && !isEndValueOriginal) {
+                return `${formatTime(startTime)} and ${formatTime(endTime)}`
+            } else if (!isStartValueOriginal) {
+                return formatTime(startTime)
+            } else if (!isEndValueOriginal) {
+                return formatTime(endTime)
+            } else {
+                return undefined
+            }
+        }
+
+        const targetYear = constructTargetYearForToleranceNotice()
+        const toleranceNotice = targetYear
+            ? {
+                  icon: TooltipFooterIcon.notice,
+                  text: makeTooltipToleranceNotice(targetYear),
+              }
+            : undefined
         const roundingNotice = series.column.roundsToSignificantFigures
             ? {
                   icon: TooltipFooterIcon.none,
@@ -680,11 +730,11 @@ export class SlopeChart
                   ),
               }
             : undefined
-        const footer = excludeUndefined([roundingNotice])
+        const footer = excludeUndefined([toleranceNotice, roundingNotice])
 
         const values = isRelativeMode
-            ? [series.endValue]
-            : [series.startValue, series.endValue]
+            ? [series.end.value]
+            : [series.start.value, series.end.value]
 
         return (
             <Tooltip
@@ -695,8 +745,9 @@ export class SlopeChart
                 offsetX={20}
                 offsetY={-16}
                 style={{ maxWidth: "250px" }}
-                title={title}
+                title={series.seriesName}
                 subtitle={timeLabel}
+                subtitleFormat={targetYear ? "notice" : undefined}
                 dissolve={fading}
                 footer={footer}
                 dismiss={() => (this.tooltipState.target = null)}
@@ -707,16 +758,35 @@ export class SlopeChart
     }
 
     private makeMissingDataLabel(series: RawSlopeChartSeries): string {
-        const { seriesName } = series
+        const { seriesName, start, end } = series
+
         const startTime = this.formatColumn.formatTime(this.startTime)
         const endTime = this.formatColumn.formatTime(this.endTime)
-        if (series.startValue === undefined && series.endValue === undefined) {
+
+        // mention the start or end value if they're missing
+        if (start?.value === undefined && end?.value === undefined) {
             return `${seriesName} (${startTime} & ${endTime})`
-        } else if (series.startValue === undefined) {
+        } else if (start?.value === undefined) {
             return `${seriesName} (${startTime})`
-        } else if (series.endValue === undefined) {
+        } else if (end?.value === undefined) {
             return `${seriesName} (${endTime})`
         }
+
+        // if both values are given but the series shows up in the No Data
+        // section, then tolerance has been applied to one of the values
+        // in such a way that we decided not to render the slope after all
+        // (e.g. when the original times are too close to each other)
+        const isToleranceAppliedToStartValue =
+            start.originalTime !== this.startTime
+        const isToleranceAppliedToEndValue = end.originalTime !== this.endTime
+        if (isToleranceAppliedToStartValue && isToleranceAppliedToEndValue) {
+            return `${seriesName} (${startTime} & ${endTime})`
+        } else if (isToleranceAppliedToStartValue) {
+            return `${seriesName} (${startTime})`
+        } else if (isToleranceAppliedToEndValue) {
+            return `${seriesName} (${endTime})`
+        }
+
         return seriesName
     }
 
diff --git a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChartConstants.ts b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChartConstants.ts
index 85cd862866..a976bed8e2 100644
--- a/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChartConstants.ts
+++ b/packages/@ourworldindata/grapher/src/slopeCharts/SlopeChartConstants.ts
@@ -1,19 +1,17 @@
-import { EntityName, PartialBy, PointVector } from "@ourworldindata/utils"
+import { PartialBy, PointVector } from "@ourworldindata/utils"
+import { EntityName, OwidVariableRow } from "@ourworldindata/types"
 import { ChartSeries } from "../chart/ChartInterface"
 import { CoreColumn } from "@ourworldindata/core-table"
 
 export interface SlopeChartSeries extends ChartSeries {
     column: CoreColumn
     entityName: EntityName
-    startValue: number
-    endValue: number
+    start: Pick<OwidVariableRow<number>, "value" | "originalTime">
+    end: Pick<OwidVariableRow<number>, "value" | "originalTime">
     annotation?: string
 }
 
-export type RawSlopeChartSeries = PartialBy<
-    SlopeChartSeries,
-    "startValue" | "endValue"
->
+export type RawSlopeChartSeries = PartialBy<SlopeChartSeries, "start" | "end">
 
 export interface PlacedSlopeChartSeries extends SlopeChartSeries {
     startPoint: PointVector
diff --git a/packages/@ourworldindata/grapher/src/stackedCharts/AbstractStackedChart.tsx b/packages/@ourworldindata/grapher/src/stackedCharts/AbstractStackedChart.tsx
index 2a5110442d..5b40a3086b 100644
--- a/packages/@ourworldindata/grapher/src/stackedCharts/AbstractStackedChart.tsx
+++ b/packages/@ourworldindata/grapher/src/stackedCharts/AbstractStackedChart.tsx
@@ -407,8 +407,8 @@ export class AbstractStackedChart
                     const pointColor =
                         row.value > 0 ? POSITIVE_COLOR : NEGATIVE_COLOR
                     return {
-                        position: row.time,
-                        time: row.time,
+                        position: row.originalTime,
+                        time: row.originalTime,
                         value: row.value,
                         valueOffset: 0,
                         interpolated:
diff --git a/packages/@ourworldindata/grapher/src/stackedCharts/MarimekkoChart.tsx b/packages/@ourworldindata/grapher/src/stackedCharts/MarimekkoChart.tsx
index 9fa7f41afd..e89b176b4d 100644
--- a/packages/@ourworldindata/grapher/src/stackedCharts/MarimekkoChart.tsx
+++ b/packages/@ourworldindata/grapher/src/stackedCharts/MarimekkoChart.tsx
@@ -383,7 +383,7 @@ export class MarimekkoChart
                             col.def.color ??
                             colorScheme.getColors(yColumns.length)[i],
                         points: col.owidRows.map((row) => ({
-                            time: row.time,
+                            time: row.originalTime,
                             position: row.entityName,
                             value: row.value,
                             valueOffset: 0,
@@ -417,7 +417,7 @@ export class MarimekkoChart
             const points: SimplePoint[] = []
             for (const row of rows) {
                 points.push({
-                    time: row.time,
+                    time: row.originalTime,
                     value: row.value,
                     entity: row.entityName,
                 })
diff --git a/packages/@ourworldindata/grapher/src/stackedCharts/StackedDiscreteBarChart.tsx b/packages/@ourworldindata/grapher/src/stackedCharts/StackedDiscreteBarChart.tsx
index c575e65c47..b298d2ae16 100644
--- a/packages/@ourworldindata/grapher/src/stackedCharts/StackedDiscreteBarChart.tsx
+++ b/packages/@ourworldindata/grapher/src/stackedCharts/StackedDiscreteBarChart.tsx
@@ -1006,7 +1006,7 @@ export class StackedDiscreteBarChart
                             col.displayName
                         ),
                         points: col.owidRows.map((row) => ({
-                            time: row.time,
+                            time: row.originalTime,
                             position: row.entityName,
                             value: row.value,
                             valueOffset: 0,
diff --git a/packages/@ourworldindata/grapher/src/tooltip/TooltipContents.tsx b/packages/@ourworldindata/grapher/src/tooltip/TooltipContents.tsx
index 3078fd31d5..a3a8b7f0f1 100644
--- a/packages/@ourworldindata/grapher/src/tooltip/TooltipContents.tsx
+++ b/packages/@ourworldindata/grapher/src/tooltip/TooltipContents.tsx
@@ -337,8 +337,12 @@ export function IconCircledS({
     )
 }
 
-export function makeTooltipToleranceNotice(targetYear: string): string {
-    return `Data not available for ${targetYear}. Showing closest available data point instead`
+export function makeTooltipToleranceNotice(
+    targetYear: string,
+    { plural }: { plural: boolean } = { plural: false }
+): string {
+    const dataPoint = plural ? "data points" : "data point"
+    return `Data not available for ${targetYear}. Showing closest available ${dataPoint} instead`
 }
 
 export function makeTooltipRoundingNotice(
diff --git a/packages/@ourworldindata/types/src/domainTypes/CoreTableTypes.ts b/packages/@ourworldindata/types/src/domainTypes/CoreTableTypes.ts
index 5fa5ba92b0..a44d6d4245 100644
--- a/packages/@ourworldindata/types/src/domainTypes/CoreTableTypes.ts
+++ b/packages/@ourworldindata/types/src/domainTypes/CoreTableTypes.ts
@@ -300,5 +300,6 @@ export interface OwidVariableRow<ValueType extends PrimitiveType> {
     entityName: EntityName
     time: Time
     value: ValueType
+    originalTime: Time
     originalValue?: ValueType
 }