diff --git a/Documentation/git-range-diff.txt b/Documentation/git-range-diff.txt
index 9701c1e5fd..a968d5237d 100644
--- a/Documentation/git-range-diff.txt
+++ b/Documentation/git-range-diff.txt
@@ -28,6 +28,17 @@ Finally, the list of matching commits is shown in the order of the
 second commit range, with unmatched commits being inserted just after
 all of their ancestors have been shown.
 
+There are three ways to specify the commit ranges:
+
+- `<range1> <range2>`: Either commit range can be of the form
+  `<base>..<rev>`, `<rev>^!` or `<rev>^-<n>`. See `SPECIFYING RANGES`
+  in linkgit:gitrevisions[7] for more details.
+
+- `<rev1>...<rev2>`. This is equivalent to
+  `<rev2>..<rev1> <rev1>..<rev2>`.
+
+- `<base> <rev1> <rev2>`: This is equivalent to `<base>..<rev1>
+  <base>..<rev2>`.
 
 OPTIONS
 -------
diff --git a/builtin/log.c b/builtin/log.c
index d0cbaaf68a..a00da91a1f 100644
--- a/builtin/log.c
+++ b/builtin/log.c
@@ -1672,7 +1672,7 @@ static void infer_range_diff_ranges(struct strbuf *r1,
 				    struct commit *head)
 {
 	const char *head_oid = oid_to_hex(&head->object.oid);
-	int prev_is_range = !!strstr(prev, "..");
+	int prev_is_range = is_range_diff_range(prev);
 
 	if (prev_is_range)
 		strbuf_addstr(r1, prev);
diff --git a/builtin/range-diff.c b/builtin/range-diff.c
index 24c4162f74..5b1f632632 100644
--- a/builtin/range-diff.c
+++ b/builtin/range-diff.c
@@ -3,6 +3,7 @@
 #include "parse-options.h"
 #include "range-diff.h"
 #include "config.h"
+#include "revision.h"
 
 static const char * const builtin_range_diff_usage[] = {
 N_("git range-diff [<options>] <old-base>..<old-tip> <new-base>..<new-tip>"),
@@ -46,12 +47,12 @@ int cmd_range_diff(int argc, const char **argv, const char *prefix)
 		diffopt.use_color = 1;
 
 	if (argc == 2) {
-		if (!strstr(argv[0], ".."))
-			die(_("no .. in range: '%s'"), argv[0]);
+		if (!is_range_diff_range(argv[0]))
+			die(_("not a commit range: '%s'"), argv[0]);
 		strbuf_addstr(&range1, argv[0]);
 
-		if (!strstr(argv[1], ".."))
-			die(_("no .. in range: '%s'"), argv[1]);
+		if (!is_range_diff_range(argv[1]))
+			die(_("not a commit range: '%s'"), argv[1]);
 		strbuf_addstr(&range2, argv[1]);
 	} else if (argc == 3) {
 		strbuf_addf(&range1, "%s..%s", argv[0], argv[1]);
diff --git a/range-diff.c b/range-diff.c
index b9950f10c8..a88612cb89 100644
--- a/range-diff.c
+++ b/range-diff.c
@@ -11,6 +11,7 @@
 #include "pretty.h"
 #include "userdiff.h"
 #include "apply.h"
+#include "revision.h"
 
 struct patch_util {
 	/* For the search for an exact match */
@@ -564,3 +565,31 @@ int show_range_diff(const char *range1, const char *range2,
 
 	return res;
 }
+
+int is_range_diff_range(const char *arg)
+{
+	char *copy = xstrdup(arg); /* setup_revisions() modifies it */
+	const char *argv[] = { "", copy, "--", NULL };
+	int i, positive = 0, negative = 0;
+	struct rev_info revs;
+
+	init_revisions(&revs, NULL);
+	if (setup_revisions(3, argv, &revs, NULL) == 1) {
+		for (i = 0; i < revs.pending.nr; i++)
+			if (revs.pending.objects[i].item->flags & UNINTERESTING)
+				negative++;
+			else
+				positive++;
+		for (i = 0; i < revs.pending.nr; i++) {
+			struct object *obj = revs.pending.objects[i].item;
+
+			if (obj->type == OBJ_COMMIT)
+				clear_commit_marks((struct commit *)obj,
+						   ALL_REV_FLAGS);
+		}
+	}
+
+	free(copy);
+	object_array_clear(&revs.pending);
+	return negative > 0 && positive > 0;
+}
diff --git a/range-diff.h b/range-diff.h
index 583ced2e8e..4abd70c40f 100644
--- a/range-diff.h
+++ b/range-diff.h
@@ -16,4 +16,10 @@ int show_range_diff(const char *range1, const char *range2,
 		    const struct diff_options *diffopt,
 		    const struct strvec *other_arg);
 
+/*
+ * Determine whether the given argument is usable as a range argument of `git
+ * range-diff`, e.g. A..B.
+ */
+int is_range_diff_range(const char *arg);
+
 #endif
diff --git a/t/t3206-range-diff.sh b/t/t3206-range-diff.sh
index ce24b5d735..b782d26820 100755
--- a/t/t3206-range-diff.sh
+++ b/t/t3206-range-diff.sh
@@ -153,6 +153,19 @@ test_expect_success 'simple A B C (unmodified)' '
 	test_cmp expect actual
 '
 
+test_expect_success 'A^! and A^-<n> (unmodified)' '
+	git range-diff --no-color topic^! unmodified^-1 >actual &&
+	cat >expect <<-EOF &&
+	1:  $(test_oid t4) = 1:  $(test_oid u4) s/12/B/
+	EOF
+	test_cmp expect actual
+'
+
+test_expect_success 'A^{/..} is not mistaken for a range' '
+	test_must_fail git range-diff topic^.. topic^{/..} 2>error &&
+	test_i18ngrep "not a commit range" error
+'
+
 test_expect_success 'trivial reordering' '
 	git range-diff --no-color main topic reordered >actual &&
 	cat >expect <<-EOF &&