diff --git a/test/basic.test.js b/test/basic.test.js
index 53ca796..636d2e0 100644
--- a/test/basic.test.js
+++ b/test/basic.test.js
@@ -791,9 +791,15 @@ for (const name in CURVES) {
           fc.property(fc.hexaString({ minLength: 64, maxLength: 64 }), (msg) => {
             const priv = C.utils.randomPrivateKey();
             const pub = C.getPublicKey(priv);
-            const sig = C.sign(msg, priv);
-            const sig2 = sig.normalizeS();
-            deepStrictEqual(sig2.hasHighS(), false);
+            const sig = C.sign(msg, priv, { lowS: false });
+            if (!sig.hasHighS()) return;
+            const sigNorm = sig.normalizeS();
+            deepStrictEqual(sigNorm.hasHighS(), false, 'a');
+
+            deepStrictEqual(C.verify(sig, msg, pub, { lowS: false }), true, 'b');
+            deepStrictEqual(C.verify(sig, msg, pub, { lowS: true }), false, 'c');
+            deepStrictEqual(C.verify(sigNorm, msg, pub, { lowS: true }), true, 'd');
+            deepStrictEqual(C.verify(sigNorm, msg, pub, { lowS: false }), true, 'e');
           }),
           { numRuns: NUM_RUNS }
         )
diff --git a/test/secp256k1.test.js b/test/secp256k1.test.js
index 66534a5..1eca6d4 100644
--- a/test/secp256k1.test.js
+++ b/test/secp256k1.test.js
@@ -200,6 +200,42 @@ describe('secp256k1', () => {
         })
       );
     });
+
+    should('.hasHighS(), .normalizeS()', () => {
+      const priv = 'c509ae2138ddca15f6b33062cd3bf76351c79f58c82ee2c2236d835bdea19d13';
+      const msg = 'b94d27b9934d3e08a52e52d7da7dabfac484efe37a5380ee9088f7ace2efcde9';
+
+      const hi =
+        'a6bf36d52da4eef85a513a88d81996a47804a2390c9910c0bd35488effca36bf8bf1f9232ab0efe4a93704ae871aa953b34d1000cef59c9d33fcc696f935108d';
+      const lo =
+        'a6bf36d52da4eef85a513a88d81996a47804a2390c9910c0bd35488effca36bf740e06dcd54f101b56c8fb5178e556ab0761cce5e053039e8bd597f5d70130b4';
+      const hi_ = new secp.Signature(
+        75421779095773161492578598757717572512754773103551662129966816753283695785663n,
+        63299015578620006752099543153250095157058828301739590985992016204296254460045n,
+        0
+      );
+      const lo_ = new secp.Signature(
+        75421779095773161492578598757717572512754773103551662129966816753283695785663n,
+        52493073658696188671471441855437812695778735977335313396613146937221907034292n,
+        0
+      );
+
+      const pub = secp.getPublicKey(priv);
+      const sig = secp.sign(msg, priv, { lowS: false });
+      deepStrictEqual(sig.hasHighS(), true);
+      deepStrictEqual(sig, hi_);
+      deepStrictEqual(sig.toCompactHex(), hi);
+
+      const lowSig = sig.normalizeS();
+      deepStrictEqual(lowSig.hasHighS(), false);
+      deepStrictEqual(lowSig, lo_);
+      deepStrictEqual(lowSig.toCompactHex(), lo);
+
+      deepStrictEqual(secp.verify(sig, msg, pub, { lowS: false }), true);
+      deepStrictEqual(secp.verify(sig, msg, pub, { lowS: true }), false);
+      deepStrictEqual(secp.verify(lowSig, msg, pub, { lowS: true }), true);
+      deepStrictEqual(secp.verify(lowSig, msg, pub, { lowS: false }), true);
+    });
   });
 
   describe('sign()', () => {