diff --git a/url/src/lib.rs b/url/src/lib.rs
index bf944741..ad9c0853 100644
--- a/url/src/lib.rs
+++ b/url/src/lib.rs
@@ -2129,7 +2129,7 @@ impl Url {
         } else {
             self.host_end
         };
-        let suffix = self.slice(old_suffix_pos..).to_owned();
+        let mut suffix = self.slice(old_suffix_pos..).to_owned();
         self.serialization.truncate(self.host_start as usize);
         if !self.has_authority() {
             debug_assert!(self.slice(self.scheme_end..self.host_start) == ":");
@@ -2143,6 +2143,23 @@ impl Url {
         self.host_end = to_u32(self.serialization.len()).unwrap();
         self.host = host.into();
 
+        // Adjust serialization to switch between host and empty segment
+        if suffix.starts_with("/.//") {
+            suffix = suffix["/.".len()..].to_string();
+            // pathname should be "//p" not "p" given that the first segment was empty
+            self.path_start -= "//".len() as u32;
+        } else if self.host == HostInternal::None && suffix.starts_with("//") {
+            if let Some(index) = self.serialization.find(":") {
+                if self.serialization.len() == index + "://".len()
+                    && self.serialization.as_bytes().get(index + 1) == Some(&b'/')
+                    && self.serialization.as_bytes().get(index + 2) == Some(&b'/')
+                {
+                    self.serialization
+                        .replace_range(index..index + "://".len(), ":/.");
+                }
+            }
+        }
+
         if let Some(new_port) = opt_new_port {
             self.port = new_port;
             if let Some(port) = new_port {
diff --git a/url/tests/expected_failures.txt b/url/tests/expected_failures.txt
index d1ed726c..9bf60b34 100644
--- a/url/tests/expected_failures.txt
+++ b/url/tests/expected_failures.txt
@@ -36,8 +36,6 @@
 <file:/.//p>
 <http://example.net/path> set hostname to <example.com:8080>
 <http://example.net:8080/path> set hostname to <example.com:>
-<non-spec:/.//p> set hostname to <h>
-<non-spec:/.//p> set hostname to <>
 <foo:///some/path> set pathname to <>
 <file:///var/log/system.log> set href to <http://0300.168.0xF0>
 <file://monkey/> set pathname to <\\\\>
diff --git a/url/tests/unit.rs b/url/tests/unit.rs
index d8bd3fc5..6febdeb2 100644
--- a/url/tests/unit.rs
+++ b/url/tests/unit.rs
@@ -1382,6 +1382,7 @@ fn serde_error_message() {
 
 #[test]
 fn test_can_be_a_base_with_set_path() {
+    use url::quirks;
     let mut url = Url::parse("web+demo:/").unwrap();
     assert!(!url.cannot_be_a_base());
 
@@ -1396,6 +1397,10 @@ fn test_can_be_a_base_with_set_path() {
     assert_eq!(segments, vec!["", "not-a-host"]);
 
     assert_eq!(url.as_str(), "web+demo:/.//not-a-host");
+    quirks::set_hostname(&mut url, "test").unwrap();
+    assert_eq!(url.as_str(), "web+demo://test//not-a-host");
+    quirks::set_hostname(&mut url, "").unwrap();
+    assert_eq!(url.as_str(), "web+demo:/.//not-a-host");
 }
 
 #[test]