diff --git a/src/policy/compiler.rs b/src/policy/compiler.rs
index b28cc03f5..31ea53062 100644
--- a/src/policy/compiler.rs
+++ b/src/policy/compiler.rs
@@ -992,9 +992,22 @@ where
                     }
                 })
                 .collect();
+
             if key_vec.len() == subs.len() && subs.len() <= 20 {
                 insert_wrap!(AstElemExt::terminal(Terminal::Multi(k, key_vec)));
             }
+            // Not a threshold, it's always more optimal to translate it to and()s as we save the
+            // resulting threshold check (N EQUAL) in any case.
+            else if k == subs.len() {
+                let mut policy = subs.first().expect("No sub policy in thresh() ?").clone();
+                for sub in &subs[1..] {
+                    policy = Concrete::And(vec![sub.clone(), policy]);
+                }
+
+                ret = best_compilations(policy_cache, &policy, sat_prob, dissat_prob)?;
+            }
+
+            // FIXME: Should we also optimize thresh(1, subs) ?
         }
     }
     for k in ret.keys() {
@@ -1153,6 +1166,7 @@ mod tests {
 
     use miniscript::{satisfy, Segwitv0};
     use policy::Liftable;
+    use script_num_size;
     use BitcoinSig;
     use DummyKey;
 
@@ -1377,6 +1391,51 @@ mod tests {
             ]
         );
     }
+
+    #[test]
+    fn compile_thresh() {
+        let (keys, _) = pubkeys_and_a_sig(21);
+
+        // Up until 20 keys, thresh should be compiled to a multi no matter the value of k
+        for k in 1..4 {
+            let small_thresh: BPolicy = policy_str!(
+                "thresh({},pk({}),pk({}),pk({}))",
+                k,
+                keys[0],
+                keys[1],
+                keys[2]
+            );
+            let small_thresh_ms: SegwitMiniScript = small_thresh.compile().unwrap();
+            let small_thresh_ms_expected: SegwitMiniScript =
+                ms_str!("multi({},{},{},{})", k, keys[0], keys[1], keys[2]);
+            assert_eq!(small_thresh_ms, small_thresh_ms_expected);
+        }
+
+        // Above 20 keys, thresh is compiled to a combination of and()s if it's a N of N,
+        // and to a ms thresh otherwise.
+        // k = 1 (or 2) does not compile, see https://github.com/rust-bitcoin/rust-miniscript/issues/114
+        for k in &[10, 15, 21] {
+            let pubkeys: Vec<Concrete<bitcoin::PublicKey>> =
+                keys.iter().map(|pubkey| Concrete::Key(*pubkey)).collect();
+            let big_thresh = Concrete::Threshold(*k, pubkeys);
+            let big_thresh_ms: SegwitMiniScript = big_thresh.compile().unwrap();
+            if *k == 21 {
+                // N * (PUSH + pubkey + CHECKSIGVERIFY)
+                assert_eq!(big_thresh_ms.script_size(), keys.len() * (1 + 33 + 1));
+            } else {
+                // N * (PUSH + pubkey + CHECKSIG + ADD + SWAP) + N EQUAL
+                assert_eq!(
+                    big_thresh_ms.script_size(),
+                    keys.len() * (1 + 33 + 3) + script_num_size(*k) + 1 - 2 // minus one SWAP and one ADD
+                );
+                let big_thresh_ms_expected = ms_str!(
+                "thresh({},pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}),s:pk({}))",
+                k, keys[0], keys[1], keys[2], keys[3], keys[4], keys[5], keys[6], keys[7], keys[8], keys[9],keys[10], keys[11], keys[12], keys[13], keys[14], keys[15], keys[16], keys[17], keys[18], keys[19], keys[20]
+            );
+                assert_eq!(big_thresh_ms, big_thresh_ms_expected);
+            };
+        }
+    }
 }
 
 #[cfg(all(test, feature = "unstable"))]