diff --git a/keypairs.js b/keypairs.js
index 730fac7..98079bd 100644
--- a/keypairs.js
+++ b/keypairs.js
@@ -237,7 +237,7 @@ Keypairs.signJws = function (opts) {
         .update(protect ? (protected64 + "." + payload64) : payload64)
         .sign(pem)
       ;
-      if (!opts.jwk || 'RSA' !== opts.jwk.kty) {
+      if ('EC' === opts.jwk.kty) {
         // ECDSA JWT signatures differ from "normal" ECDSA signatures
         // https://tools.ietf.org/html/rfc7518#section-3.4
         binsig = convertIfEcdsa(binsig);
@@ -259,31 +259,37 @@ Keypairs.signJws = function (opts) {
 
     function convertIfEcdsa(binsig) {
       // should have asn1 sequence header of 0x30
-      if (0x30 !== binsig[0]) { return binsig; }
+      if (0x30 !== binsig[0]) { throw new Error("Impossible EC SHA head marker"); }
       var index = 2; // first ecdsa "R" header byte
       var len = binsig[1];
       var lenlen = 0;
       // Seek length of length if length is greater than 127 (i.e. two 512-bit / 64-byte R and S values)
       if (0x80 & len) {
-        lenlen = len - 0x80;
-        // the length of the signature won't be over 256 bytes (2048 bits) for many years yet
-        if (1 !== lenlen) { return binsig; }
-        // the length is this number
-        len = binsig[2];
+        lenlen = len - 0x80; // should be exactly 1
+        len = binsig[2]; // should be <= 130 (two 64-bit SHA-512s, plus padding)
         index += lenlen;
       }
-      // should have bigint header of 0x02 followd by a single byte of length
-      if (0x02 !== binsig[index]) { return binsig; }
+      // should be of BigInt type
+      if (0x02 !== binsig[index]) { throw new Error("Impossible EC SHA R marker"); }
       index += 1;
+
       var rlen = binsig[index];
-      var r = binsig.slice(index + 1, index + 1 + rlen);
+      var bits = 32;
+      if (rlen > 49) {
+        bits = 64;
+      } else if (rlen > 33) {
+        bits = 48;
+      }
+      var r = binsig.slice(index + 1, index + 1 + rlen).toString('hex');
       var slen = binsig[index + 1 + rlen + 1]; // skip header and read length
-      var s = binsig.slice(index + 1 + rlen + 1 + 1);
-      if (slen !== s.byteLength) { return binsig; }
+      var s = binsig.slice(index + 1 + rlen + 1 + 1).toString('hex');
+      if (2 *slen !== s.length) { throw new Error("Impossible EC SHA S length"); }
       // There may be one byte of padding on either
-      if (33 === r.byteLength) { r = r.slice(1); }
-      if (33 === s.byteLength) { s = s.slice(1); }
-      return Buffer.concat([r, s]);
+      while (r.length < 2*bits) { r = '00' + r; }
+      while (s.length < 2*bits) { s = '00' + s; }
+      if (2*(bits+1) === r.length) { r = r.slice(2); }
+      if (2*(bits+1) === s.length) { s = s.slice(2); }
+      return Buffer.concat([Buffer.from(r, 'hex'), Buffer.from(s, 'hex')]);
     }
 
     if (opts.pem && opts.jwk) {
diff --git a/package.json b/package.json
index 775bbca..24dd99c 100644
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "keypairs",
-  "version": "1.2.11",
+  "version": "1.2.12",
   "description": "Lightweight RSA/ECDSA keypair generation and JWK <-> PEM",
   "main": "keypairs.js",
   "files": [