diff --git a/src/string.rs b/src/string.rs
index 734cd81..636c725 100644
--- a/src/string.rs
+++ b/src/string.rs
@@ -164,19 +164,25 @@ where
     }
 }
 
-impl PartialEq<String> for String {
+impl PartialEq for String {
     fn eq(&self, other: &String) -> bool {
         self.as_bytes() == other.as_bytes()
     }
 }
 
-impl PartialEq<&String> for String {
-    fn eq(&self, other: &&String) -> bool {
-        self.as_bytes() == other.as_bytes()
+impl Eq for String {}
+
+impl PartialOrd for String {
+    fn partial_cmp(&self, other: &String) -> Option<cmp::Ordering> {
+        self.as_bytes().partial_cmp(&other.as_bytes())
     }
 }
 
-impl Eq for String {}
+impl Ord for String {
+    fn cmp(&self, other: &String) -> cmp::Ordering {
+        self.as_bytes().cmp(&other.as_bytes())
+    }
+}
 
 impl Hash for String {
     fn hash<H: Hasher>(&self, state: &mut H) {
@@ -244,6 +250,8 @@ where
     }
 }
 
+impl Eq for BorrowedStr<'_> {}
+
 impl<T> PartialOrd<T> for BorrowedStr<'_>
 where
     T: AsRef<str>,
@@ -253,6 +261,12 @@ where
     }
 }
 
+impl Ord for BorrowedStr<'_> {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        self.0.cmp(other.0)
+    }
+}
+
 /// A borrowed byte slice (`&[u8]`) that holds a strong reference to the Lua state.
 pub struct BorrowedBytes<'a>(&'a [u8], #[allow(unused)] Lua);
 
@@ -294,6 +308,8 @@ where
     }
 }
 
+impl Eq for BorrowedBytes<'_> {}
+
 impl<T> PartialOrd<T> for BorrowedBytes<'_>
 where
     T: AsRef<[u8]>,
@@ -303,6 +319,12 @@ where
     }
 }
 
+impl Ord for BorrowedBytes<'_> {
+    fn cmp(&self, other: &Self) -> cmp::Ordering {
+        self.0.cmp(other.0)
+    }
+}
+
 impl<'a> IntoIterator for BorrowedBytes<'a> {
     type Item = &'a u8;
     type IntoIter = slice::Iter<'a, u8>;
diff --git a/tests/conversion.rs b/tests/conversion.rs
index 5ca9982..d0e7a07 100644
--- a/tests/conversion.rs
+++ b/tests/conversion.rs
@@ -33,7 +33,7 @@ fn test_string_into_lua() -> Result<()> {
     // Direct conversion
     let s = lua.create_string("hello, world!")?;
     let s2 = (&s).into_lua(&lua)?;
-    assert_eq!(s, s2.as_string().unwrap());
+    assert_eq!(s, *s2.as_string().unwrap());
 
     // Push into stack
     let table = lua.create_table()?;