diff --git a/object-name.c b/object-name.c
index 2dc5d2549b8..4d2746574cd 100644
--- a/object-name.c
+++ b/object-name.c
@@ -1832,7 +1832,8 @@ static void diagnose_invalid_index_path(struct repository *r,
 		pos = -pos - 1;
 	if (pos < istate->cache_nr) {
 		ce = istate->cache[pos];
-		if (ce_namelen(ce) == namelen &&
+		if (!S_ISSPARSEDIR(ce->ce_mode) &&
+		    ce_namelen(ce) == namelen &&
 		    !memcmp(ce->name, filename, namelen))
 			die(_("path '%s' is in the index, but not at stage %d\n"
 			    "hint: Did you mean ':%d:%s'?"),
@@ -1848,7 +1849,8 @@ static void diagnose_invalid_index_path(struct repository *r,
 		pos = -pos - 1;
 	if (pos < istate->cache_nr) {
 		ce = istate->cache[pos];
-		if (ce_namelen(ce) == fullname.len &&
+		if (!S_ISSPARSEDIR(ce->ce_mode) &&
+		    ce_namelen(ce) == fullname.len &&
 		    !memcmp(ce->name, fullname.buf, fullname.len))
 			die(_("path '%s' is in the index, but not '%s'\n"
 			    "hint: Did you mean ':%d:%s' aka ':%d:./%s'?"),
diff --git a/t/t1092-sparse-checkout-compatibility.sh b/t/t1092-sparse-checkout-compatibility.sh
index 08c9cfd359e..fa1d5603605 100755
--- a/t/t1092-sparse-checkout-compatibility.sh
+++ b/t/t1092-sparse-checkout-compatibility.sh
@@ -1158,15 +1158,21 @@ test_expect_success 'show (cached blobs/trees)' '
 	test_all_match git show :deep/a &&
 	test_sparse_match git show :folder1/a &&
 
-	# Asking "git show" for directories in the index
-	# had different behavior depending on the existence
-	# of a sparse index.
+	# The error message differs depending on whether
+	# the directory exists in the worktree.
 	test_all_match test_must_fail git show :deep/ &&
 	test_must_fail git -C full-checkout show :folder1/ &&
-	test_must_fail git -C sparse-checkout show :folder1/ &&
+	test_sparse_match test_must_fail git show :folder1/ &&
 
-	test_must_fail git -C sparse-index show :folder1/ 2>err &&
-	grep "is in the index, but not at stage 0" err
+	# Change the sparse cone for an extra case:
+	run_on_sparse git sparse-checkout set deep/deeper1 &&
+
+	# deep/deeper2 is a sparse directory in the sparse index.
+	test_sparse_match test_must_fail git show :deep/deeper2/ &&
+
+	# deep/deeper2/deepest is not in the sparse index, but
+	# will trigger an index expansion.
+	test_sparse_match test_must_fail git show :deep/deeper2/deepest/
 '
 
 test_expect_success 'submodule handling' '