diff --git a/DESCRIPTION b/DESCRIPTION
index def576fa6..341742774 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Type: Package
 Package: parameters
 Title: Processing of Model Parameters
-Version: 0.21.3.8
+Version: 0.21.3.9
 Authors@R:
     c(person(given = "Daniel",
              family = "Lüdecke",
diff --git a/NEWS.md b/NEWS.md
index 4231e793d..fdf73cf56 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -24,6 +24,9 @@
 * `print(include_reference = TRUE)` for `model_parameters()` did not work when
   run inside a pipe-chain.
 
+* Fixed issues with `format()` for objects returned by `compare_parameters()`
+  that included mixed models.
+
 # parameters 0.21.3
 
 ## Changes
diff --git a/R/compare_parameters.R b/R/compare_parameters.R
index 203d10915..70048b324 100644
--- a/R/compare_parameters.R
+++ b/R/compare_parameters.R
@@ -98,7 +98,7 @@ compare_parameters <- function(...,
       names(models) <- model_names
     }
   } else {
-    model_names <- match.call(expand.dots = FALSE)$`...`
+    model_names <- match.call(expand.dots = FALSE)[["..."]]
     if (length(names(model_names)) > 0) {
       model_names <- names(model_names)
     } else if (any(vapply(model_names, is.call, TRUE))) {
@@ -275,14 +275,14 @@ compare_models <- compare_parameters
       }
     } else {
       match_pretty_names <- att$pretty_names[x$Parameter]
-      if (!anyNA(match_pretty_names)) {
-        x$Parameter <- att$pretty_names[x$Parameter]
-      } else {
+      if (anyNA(match_pretty_names)) {
         match_pretty_names <- match(names(att$pretty_names), x$Parameter)
         match_pretty_names <- match_pretty_names[!is.na(match_pretty_names)]
         if (length(match_pretty_names)) {
           x$Parameter[match_pretty_names] <- att$pretty_names[x$Parameter[match_pretty_names]]
         }
+      } else {
+        x$Parameter <- att$pretty_names[x$Parameter]
       }
     }
   }
diff --git a/R/format.R b/R/format.R
index 68bbab5d9..c160924c9 100644
--- a/R/format.R
+++ b/R/format.R
@@ -426,6 +426,13 @@ format.compare_parameters <- function(x,
     formatted_table <- split(out, f = split_by)
     formatted_table <- lapply(names(formatted_table), function(tab) {
       i <- formatted_table[[tab]]
+      # check if data frame is empty - this may happen if not all combinations
+      # of split_by factors are present in the data (e.g., zero-inflated mixed
+      # models, that have random effects for the count, but not for the zero-
+      # inflation component)
+      if (nrow(i) == 0L) {
+        return(NULL)
+      }
       # remove unique columns
       if (insight::n_unique(i$Component) == 1L) i$Component <- NULL
       if (insight::n_unique(i$Effects) == 1L) i$Effects <- NULL
@@ -447,6 +454,9 @@ format.compare_parameters <- function(x,
       i
     })
 
+    # remove empty tables
+    formatted_table <- insight::compact_list(formatted_table)
+
     # for HTML, bind data frames
     if (identical(format, "html")) {
       # fix non-equal length of columns and bind data frames
diff --git a/R/utils_format.R b/R/utils_format.R
index 968e01e29..9b140cb04 100644
--- a/R/utils_format.R
+++ b/R/utils_format.R
@@ -328,9 +328,12 @@
 }
 
 
-.add_reference_level <- function(params) {
-  # check if we have a model object, else return parameter table
-  model <- .get_object(params)
+.add_reference_level <- function(params, model = NULL) {
+  if (is.null(model)) {
+    # check if we have a model object, if not provided by user
+    model <- .get_object(params)
+  }
+  # no model object provided? Try to get data from model call
   if (is.null(model)) {
     # get data from model call
     model_data <- .safe(eval(attributes(params)$model_call$data))
diff --git a/tests/testthat/test-format_model_parameters.R b/tests/testthat/test-format_model_parameters.R
index 1e7b1ebfc..6e007f864 100644
--- a/tests/testthat/test-format_model_parameters.R
+++ b/tests/testthat/test-format_model_parameters.R
@@ -173,3 +173,32 @@ withr::with_options(
     })
   }
 )
+
+skip_if_not_installed("lme4")
+skip_if_not_installed("glmmTMB")
+
+test_that("format, compare_parameters, mixed models", {
+  data(mtcars)
+  data(Salamanders, package = "glmmTMB")
+  model1 <- lme4::lmer(mpg ~ wt + (1 | gear), data = mtcars)
+  model2 <- glmmTMB::glmmTMB(
+    count ~ spp + mined + (1 | site),
+    ziformula = ~mined,
+    family = poisson(),
+    data = Salamanders
+  )
+  out <- compare_parameters(model1, model2, effects = "all", component = "all")
+  f <- format(out)
+  expect_length(f, 3)
+  f <- format(out, format = "html")
+  expect_identical(
+    f$Component,
+    c(
+      "Fixed Effects", "Fixed Effects", "Fixed Effects", "Fixed Effects",
+      "Fixed Effects", "Fixed Effects", "Fixed Effects", "Fixed Effects",
+      "Fixed Effects", "Fixed Effects (Zero-Inflation Component)",
+      "Fixed Effects (Zero-Inflation Component)", "Random Effects",
+      "Random Effects", "Random Effects"
+    )
+  )
+})