diff --git a/src/descriptor/mod.rs b/src/descriptor/mod.rs
index 1a2a7da16..487bbcc45 100644
--- a/src/descriptor/mod.rs
+++ b/src/descriptor/mod.rs
@@ -1036,6 +1036,21 @@ mod tests {
         );
     }
 
+    #[test]
+    fn display_prefers_u() {
+        // The fragments u:0 and l:0 are identical in terms of Script and
+        // in terms of the in-memory representation -- OrI(False, False).
+        // Test that the way we display the ambiguous fragment doesn't
+        // change, in case somebody somehow is depending on it.
+        let desc = StdDescriptor::from_str("sh(u:0)").unwrap();
+        assert_eq!("sh(u:0)#ncq3yf9h", desc.to_string());
+
+        // This is a regression test for https://github.com/rust-bitcoin/rust-miniscript/pull/735
+        // which was found at the same time. It's just a bug plain and simple.
+        let desc = StdDescriptor::from_str("sh(and_n(u:0,1))").unwrap();
+        assert_eq!("sh(and_n(u:0,1))#5j5tw8nm", desc.to_string());
+    }
+
     #[test]
     fn desc_rtt_tests() {
         roundtrip_descriptor("c:pk_k()");
@@ -2011,6 +2026,30 @@ pk(03f28773c2d975288bc7d1d205c3748651b075fbc6610e58cddeeddf8f19405aa8))";
         Descriptor::<DescriptorPublicKey>::from_str("wsh(andor(pk(tpubDEN9WSToTyy9ZQfaYqSKfmVqmq1VVLNtYfj3Vkqh67et57eJ5sTKZQBkHqSwPUsoSskJeaYnPttHe2VrkCsKA27kUaN9SDc5zhqeLzKa1rr/0'/<0;1;2;3>/*),older(10000),pk(tpubD8LYfn6njiA2inCoxwM7EuN3cuLVcaHAwLYeups13dpevd3nHLRdK9NdQksWXrhLQVxcUZRpnp5CkJ1FhE61WRAsHxDNAkvGkoQkAeWDYjV/8/<0;1;2>/*)))").unwrap_err();
     }
 
+    #[test]
+    fn regression_736() {
+        Descriptor::<DescriptorPublicKey>::from_str(
+            "tr(0000000000000000000000000000000000000000000000000000000000000002,)",
+        )
+        .unwrap_err();
+    }
+
+    #[test]
+    fn regression_734() {
+        Descriptor::<DescriptorPublicKey>::from_str(
+            "wsh(or_i(pk(0202baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa0a66a),1))",
+        )
+        .unwrap();
+        Descriptor::<DescriptorPublicKey>::from_str(
+            "sh(or_i(pk(0202baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa0a66a),1))",
+        )
+        .unwrap();
+        Descriptor::<DescriptorPublicKey>::from_str(
+            "tr(02baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa0a66a,1)",
+        )
+        .unwrap_err();
+    }
+
     #[test]
     fn test_context_pks() {
         let comp_key = bitcoin::PublicKey::from_str(
diff --git a/src/descriptor/tr.rs b/src/descriptor/tr.rs
index 2f505780c..41845f174 100644
--- a/src/descriptor/tr.rs
+++ b/src/descriptor/tr.rs
@@ -603,9 +603,6 @@ fn parse_tr_tree(s: &str) -> Result<expression::Tree, Error> {
             return Err(Error::Unexpected("invalid taproot internal key".to_string()));
         }
         let internal_key = expression::Tree { name: key.name, args: vec![] };
-        if script.is_empty() {
-            return Ok(expression::Tree { name: "tr", args: vec![internal_key] });
-        }
         let (tree, rest) = expression::Tree::from_slice_delim(script, 1, '{')?;
         if rest.is_empty() {
             Ok(expression::Tree { name: "tr", args: vec![internal_key, tree] })
diff --git a/src/miniscript/display.rs b/src/miniscript/display.rs
index 2a4e9f757..c6510b7d0 100644
--- a/src/miniscript/display.rs
+++ b/src/miniscript/display.rs
@@ -260,14 +260,14 @@ impl<Pk: MiniscriptKey, Ctx: ScriptContext> Terminal<Pk, Ctx> {
             Terminal::ZeroNotEqual(..) => "n",
             Terminal::AndV(_, ref r) if matches!(r.as_inner(), Terminal::True) => "t",
             Terminal::AndV(..) => "and_v",
-            Terminal::AndB(..) => "and_b",
             Terminal::AndOr(_, _, ref c) if matches!(c.as_inner(), Terminal::False) => "and_n",
+            Terminal::AndB(..) => "and_b",
             Terminal::AndOr(..) => "andor",
             Terminal::OrB(..) => "or_b",
             Terminal::OrD(..) => "or_d",
             Terminal::OrC(..) => "or_c",
-            Terminal::OrI(ref l, _) if matches!(l.as_inner(), Terminal::False) => "l",
             Terminal::OrI(_, ref r) if matches!(r.as_inner(), Terminal::False) => "u",
+            Terminal::OrI(ref l, _) if matches!(l.as_inner(), Terminal::False) => "l",
             Terminal::OrI(..) => "or_i",
             Terminal::Thresh(..) => "thresh",
             Terminal::Multi(..) => "multi",