diff --git a/encoding/jsonschema/constraints.go b/encoding/jsonschema/constraints.go
index c6684ed68..357d93406 100644
--- a/encoding/jsonschema/constraints.go
+++ b/encoding/jsonschema/constraints.go
@@ -84,15 +84,18 @@ var constraints = []*constraint{
 	p2("dependencies", constraintDependencies),
 	todo("dependentRequired", vfrom(VersionDraft2019_09)),
 	todo("dependentSchemas", vfrom(VersionDraft2019_09)),
-	p2("deprecated", constraintDeprecated),
+	p2d("deprecated", constraintDeprecated, vfrom(VersionDraft2019_09)),
 	p2("description", constraintDescription),
+	todo("discriminator", vset(VersionOpenAPI3_0)),
 	todo("else", vfrom(VersionDraft7)),
 	p2("enum", constraintEnum),
+	todo("example", vset(VersionOpenAPI3_0)),
 	p2d("examples", constraintExamples, vfrom(VersionDraft6)),
 	p2("exclusiveMaximum", constraintExclusiveMaximum),
 	p2("exclusiveMinimum", constraintExclusiveMinimum),
+	todo("externalDocs", vset(VersionOpenAPI3_0)),
 	todo("format", allVersions),
-	p1d("id", constraintID, vto(VersionDraft4)),
+	p1d("id", constraintID, vto(VersionDraft4)&^openAPI3_0),
 	todo("if", vfrom(VersionDraft7)),
 	p2("items", constraintItems),
 	p1d("maxContains", constraintMaxContains, vfrom(VersionDraft2019_09)),
@@ -107,7 +110,7 @@ var constraints = []*constraint{
 	p3("minimum", constraintMinimum),
 	p2("multipleOf", constraintMultipleOf),
 	p3("not", constraintNot),
-	p2("nullable", constraintNullable),
+	p2d("nullable", constraintNullable, vset(VersionOpenAPI3_0)),
 	p3("oneOf", constraintOneOf),
 	p2("pattern", constraintPattern),
 	p3("patternProperties", constraintPatternProperties),
@@ -123,6 +126,7 @@ var constraints = []*constraint{
 	todo("unevaluatedProperties", vfrom(VersionDraft2019_09)),
 	p2("uniqueItems", constraintUniqueItems),
 	todo("writeOnly", vfrom(VersionDraft7)),
+	todo("xml", vset(VersionOpenAPI3_0)),
 }
 
 func todo(name string, versions versionSet) *constraint {
diff --git a/encoding/jsonschema/version.go b/encoding/jsonschema/version.go
index 88656adbc..b3f9994f5 100644
--- a/encoding/jsonschema/version.go
+++ b/encoding/jsonschema/version.go
@@ -30,13 +30,21 @@ const (
 	VersionDraft7       // http://json-schema.org/draft-07/schema#
 	VersionDraft2019_09 // https://json-schema.org/draft/2019-09/schema
 	VersionDraft2020_12 // https://json-schema.org/draft/2020-12/schema
+	VersionOpenAPI3_0   // OpenAPI 3.0
 
 	numVersions // unknown
 )
 
+var (
+	openAPI3_0    = vset(VersionOpenAPI3_0)
+	notOpenAPI3_0 = allVersions &^ vset(VersionOpenAPI3_0)
+)
+
 type versionSet int
 
-const allVersions = versionSet(1<<numVersions-1) &^ (1 << VersionUnknown)
+// allVersions includes all regular versions of JSON Schema.
+// It does not include OpenAPI v3.0
+const allVersions = versionSet(1<<numVersions-1) &^ (1 << VersionUnknown) &^ (1 << VersionOpenAPI3_0)
 
 // contains reports whether m contains the version v.
 func (m versionSet) contains(v Version) bool {
@@ -70,7 +78,9 @@ func ParseVersion(sv string) (Version, error) {
 	// If this linear search is ever a performance issue, we could
 	// build a map, but it doesn't seem worthwhile for now.
 	for i := Version(1); i < numVersions; i++ {
-		if sv == i.String() {
+		// Note: OpenAPI doesn't have a schema URI in the
+		// same way as the other schema versions.
+		if i != VersionOpenAPI3_0 && sv == i.String() {
 			return i, nil
 		}
 	}
diff --git a/encoding/jsonschema/version_string.go b/encoding/jsonschema/version_string.go
index a11d047b3..8eb87e397 100644
--- a/encoding/jsonschema/version_string.go
+++ b/encoding/jsonschema/version_string.go
@@ -14,12 +14,13 @@ func _() {
 	_ = x[VersionDraft7-3]
 	_ = x[VersionDraft2019_09-4]
 	_ = x[VersionDraft2020_12-5]
-	_ = x[numVersions-6]
+	_ = x[VersionOpenAPI3_0-6]
+	_ = x[numVersions-7]
 }
 
-const _Version_name = "unknownhttp://json-schema.org/draft-04/schema#http://json-schema.org/draft-06/schema#http://json-schema.org/draft-07/schema#https://json-schema.org/draft/2019-09/schemahttps://json-schema.org/draft/2020-12/schemaunknown"
+const _Version_name = "unknownhttp://json-schema.org/draft-04/schema#http://json-schema.org/draft-06/schema#http://json-schema.org/draft-07/schema#https://json-schema.org/draft/2019-09/schemahttps://json-schema.org/draft/2020-12/schemaOpenAPI 3.0unknown"
 
-var _Version_index = [...]uint8{0, 7, 46, 85, 124, 168, 212, 219}
+var _Version_index = [...]uint8{0, 7, 46, 85, 124, 168, 212, 223, 230}
 
 func (i Version) String() string {
 	if i < 0 || i >= Version(len(_Version_index)-1) {
diff --git a/encoding/openapi/decode.go b/encoding/openapi/decode.go
index d60e82d68..84fc0cfb8 100644
--- a/encoding/openapi/decode.go
+++ b/encoding/openapi/decode.go
@@ -15,6 +15,7 @@
 package openapi
 
 import (
+	"fmt"
 	"strings"
 
 	"cuelang.org/go/cue"
@@ -41,15 +42,24 @@ func Extract(data cue.InstanceOrValue, c *Config) (*ast.File, error) {
 		}
 	}
 
-	js, err := jsonschema.Extract(data, &jsonschema.Config{
-		Root: oapiSchemas,
-		Map:  openAPIMapping,
-	})
+	v := data.Value()
+	versionValue := v.LookupPath(cue.MakePath(cue.Str("openapi")))
+	if versionValue.Err() != nil {
+		return nil, fmt.Errorf("openapi field is required but not found")
+	}
+	version, err := versionValue.String()
 	if err != nil {
-		return nil, err
+		return nil, fmt.Errorf("invalid openapi field (must be string): %v", err)
+	}
+	var schemaVersion jsonschema.Version
+	switch {
+	case strings.HasPrefix(version, "v3.0."):
+		schemaVersion = jsonschema.OpenAPI3_0
+	case strings.HasPrefix(version, "v3.1."):
+		schemaVersion = VersionDraft2020_12
+	default:
+		return nil, fmt.Errorf("unknown OpenAPI version %q", version)
 	}
-
-	v := data.Value()
 
 	doc, _ := v.LookupPath(cue.MakePath(cue.Str("info"), cue.Str("title"))).String() // Required
 	if s, _ := v.LookupPath(cue.MakePath(cue.Str("info"), cue.Str("description"))).String(); s != "" {
@@ -65,6 +75,14 @@ func Extract(data cue.InstanceOrValue, c *Config) (*ast.File, error) {
 		add(cg)
 	}
 
+	js, err := jsonschema.Extract(data, &jsonschema.Config{
+		Root:           oapiSchemas,
+		Map:            openAPIMapping,
+		DefaultVersion: schemaVersion,
+	})
+	if err != nil {
+		return nil, err
+	}
 	preamble := js.Preamble()
 	body := js.Decls[len(preamble):]
 	for _, d := range preamble {