diff --git a/lib/urlapi.c b/lib/urlapi.c
index a5ec95032b..d92887bf88 100644
--- a/lib/urlapi.c
+++ b/lib/urlapi.c
@@ -1721,8 +1721,11 @@ static CURLUcode set_url(CURLU *u, const char *url, size_t part_size,
        and this is a redirect */
     uc = curl_url_get(u, CURLUPART_URL, &oldurl, flags);
     if(!uc) {
-      /* success, meaning the "" is a fine relative URL, but nothing
-         changes */
+      /* success, meaning the "" is a fine relative URL, and the new URL
+         inherits scheme/authority/path/query, but not fragment, from the
+         existing URL (RFC 3986 section 5.2.2) */
+      curlx_safefree(u->fragment);
+      u->fragment_present = FALSE;
       curlx_free(oldurl);
       return CURLUE_OK;
     }
diff --git a/tests/data/test1560 b/tests/data/test1560
index e27229739f..7f78aece2f 100644
--- a/tests/data/test1560
+++ b/tests/data/test1560
@@ -37,7 +37,7 @@ lib%TESTNUMBER
 success
 </stdout>
 <limits>
-Allocations: 3200
+Allocations: 3250
 </limits>
 </verify>
 </testcase>
diff --git a/tests/libtest/lib1560.c b/tests/libtest/lib1560.c
index bdf8b56cad..a62d9334b2 100644
--- a/tests/libtest/lib1560.c
+++ b/tests/libtest/lib1560.c
@@ -1356,6 +1356,33 @@ static const struct redircase set_url_list[] = {
    "", /* blank redirect */
    "https://example.com/",
    0, 0, CURLUE_OK },
+  {"file:///test?test#test",
+   "", "file:///test?test",
+   0, 0, CURLUE_OK},
+  {"https://example.com/path?query#frag",
+   "", "https://example.com/path?query",
+   0, 0, CURLUE_OK},
+  {"ftp://example.com/dir/file#anchor",
+   "", "ftp://example.com/dir/file",
+   0, 0, CURLUE_OK},
+  {"http://example.com/path#frag",
+   "", "http://example.com/path",
+   0, 0, CURLUE_OK},
+  {"http://example.com/#frag",
+   "", "http://example.com/",
+   0, 0, CURLUE_OK},
+  {"http://user:pass@example.com/path?query#frag",
+   "", "http://user:pass@example.com/path?query",
+   0, 0, CURLUE_OK},
+  {"http://example.com:8080/path?query#frag",
+   "", "http://example.com:8080/path?query",
+   0, 0, CURLUE_OK},
+  {"https://user:pass@example.com:8443/path?query#frag",
+   "", "https://user:pass@example.com:8443/path?query",
+   0, 0, CURLUE_OK},
+  {"http://[::1]/path#frag",
+   "", "http://[::1]/path",
+   0, 0, CURLUE_OK},
   {"http://firstplace.example.com/want/1314",
    "//somewhere.example.com/reply/1314",
    "http://somewhere.example.com/reply/1314",