diff --git a/url/src/lib.rs b/url/src/lib.rs
index 0be004e6f..632aa702f 100644
--- a/url/src/lib.rs
+++ b/url/src/lib.rs
@@ -683,7 +683,14 @@ impl Url {
             assert_eq!(self.host_end, self.scheme_end + 1);
             assert_eq!(self.host, HostInternal::None);
             assert_eq!(self.port, None);
-            assert_eq!(self.path_start, self.scheme_end + 1);
+            if self.path().starts_with("//") {
+                // special case when first path fragment is empty
+                assert_eq!(self.byte_at(self.scheme_end + 1), b'/');
+                assert_eq!(self.byte_at(self.scheme_end + 2), b'.');
+                assert_eq!(self.path_start, self.scheme_end + 3);
+            } else {
+                assert_eq!(self.path_start, self.scheme_end + 1);
+            }
         }
         if let Some(start) = self.query_start {
             assert!(start >= self.path_start);
diff --git a/url/src/parser.rs b/url/src/parser.rs
index 7829e03a0..57b7181f5 100644
--- a/url/src/parser.rs
+++ b/url/src/parser.rs
@@ -467,19 +467,28 @@ impl<'a> Parser<'a> {
             return self.after_double_slash(input, scheme_type, scheme_end);
         }
         // Anarchist URL (no authority)
-        let path_start = to_u32(self.serialization.len())?;
+        let mut path_start = to_u32(self.serialization.len())?;
         let username_end = path_start;
         let host_start = path_start;
         let host_end = path_start;
         let host = HostInternal::None;
         let port = None;
         let remaining = if let Some(input) = input.split_prefix('/') {
-            let path_start = self.serialization.len();
             self.serialization.push('/');
-            self.parse_path(scheme_type, &mut false, path_start, input)
+            self.parse_path(scheme_type, &mut false, path_start as usize, input)
         } else {
             self.parse_cannot_be_a_base_path(input)
         };
+        // This prevents web+demo:/.//not-a-host/ or web+demo:/path/..//not-a-host/,
+        // when parsed and then serialized, from ending up as web+demo://not-a-host/
+        // (they end up as web+demo:/.//not-a-host/).
+        if self.serialization[path_start as usize..].starts_with("//") {
+            // If url’s host is null, url does not have an opaque path,
+            // url’s path’s size is greater than 1, and url’s path[0] is the empty string,
+            // then append U+002F (/) followed by U+002E (.) to output.
+            self.serialization.insert_str(path_start as usize, "/.");
+            path_start += 2;
+        }
         self.with_query_and_fragment(
             scheme_type,
             scheme_end,
@@ -1281,16 +1290,6 @@ impl<'a> Parser<'a> {
             self.serialization.push_str(path.trim_start_matches('/'));
         }
 
-        // This prevents web+demo:/.//not-a-host/ or web+demo:/path/..//not-a-host/,
-        // when parsed and then serialized, from ending up as web+demo://not-a-host/
-        // (they end up as web+demo:/.//not-a-host/).
-        if !*has_host && self.serialization[path_start..].starts_with("//") {
-            // If url’s host is null, url does not have an opaque path,
-            // url’s path’s size is greater than 1, and url’s path[0] is the empty string,
-            // then append U+002F (/) followed by U+002E (.) to output.
-            self.serialization.insert_str(path_start, "/.");
-        }
-
         input
     }
 
diff --git a/url/src/slicing.rs b/url/src/slicing.rs
index a90337bb6..c2e441ef2 100644
--- a/url/src/slicing.rs
+++ b/url/src/slicing.rs
@@ -149,7 +149,14 @@ impl Url {
                 }
             }
 
-            Position::AfterPort => self.path_start as usize,
+            Position::AfterPort => {
+                if let Some(port) = self.port {
+                    debug_assert!(self.byte_at(self.host_end) == b':');
+                    self.host_end as usize + ":".len() + port.to_string().len()
+                } else {
+                    self.host_end as usize
+                }
+            }
 
             Position::BeforePath => self.path_start as usize,
 
diff --git a/url/tests/urltestdata.json b/url/tests/urltestdata.json
index 8bda080a9..1a352bff1 100644
--- a/url/tests/urltestdata.json
+++ b/url/tests/urltestdata.json
@@ -7487,7 +7487,6 @@
     "hash": ""
   },
   "Serialize /. in path",
-  "skip next",
   {
     "input": "non-spec:/.//",
     "base": "about:blank",
@@ -7502,7 +7501,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "non-spec:/..//",
     "base": "about:blank",
@@ -7517,7 +7515,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "non-spec:/a/..//",
     "base": "about:blank",
@@ -7532,7 +7529,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "non-spec:/.//path",
     "base": "about:blank",
@@ -7547,7 +7543,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "non-spec:/..//path",
     "base": "about:blank",
@@ -7562,7 +7557,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "non-spec:/a/..//path",
     "base": "about:blank",
@@ -7637,7 +7631,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "",
     "base": "non-spec:/..//p",
@@ -7652,7 +7645,6 @@
     "search": "",
     "hash": ""
   },
-  "skip next",
   {
     "input": "path",
     "base": "non-spec:/..//p",