diff --git a/apply.c b/apply.c
index fed195250b..afc1c6510e 100644
--- a/apply.c
+++ b/apply.c
@@ -3582,7 +3582,9 @@ static int try_threeway(struct apply_state *state,
 
 	/* No point falling back to 3-way merge in these cases */
 	if (patch->is_delete ||
-	    S_ISGITLINK(patch->old_mode) || S_ISGITLINK(patch->new_mode))
+	    S_ISGITLINK(patch->old_mode) || S_ISGITLINK(patch->new_mode) ||
+	    (patch->is_new && !patch->direct_to_threeway) ||
+	    (patch->is_rename && !patch->lines_added && !patch->lines_deleted))
 		return -1;
 
 	/* Preimage the patch was prepared for */
diff --git a/t/t4108-apply-threeway.sh b/t/t4108-apply-threeway.sh
index cc3aa3314a..c558282bc0 100755
--- a/t/t4108-apply-threeway.sh
+++ b/t/t4108-apply-threeway.sh
@@ -275,4 +275,22 @@ test_expect_success 'apply full-index patch with 3way' '
 	git apply --3way --index bin.diff
 '
 
+test_expect_success 'apply delete then new patch with 3way' '
+	git reset --hard main &&
+	test_write_lines 2 > delnew &&
+	git add delnew &&
+	git diff --cached >> new.patch &&
+	git reset --hard &&
+	test_write_lines 1 > delnew &&
+	git add delnew &&
+	git commit -m "delnew" &&
+	rm delnew &&
+	git diff >> delete-then-new.patch &&
+	cat new.patch >> delete-then-new.patch &&
+
+	git checkout -- . &&
+	# Apply must succeed.
+	git apply --3way delete-then-new.patch
+'
+
 test_done