diff --git a/src/script/interpreter.cpp b/src/script/interpreter.cpp
index 3128bae35f..e049fed2e5 100644
--- a/src/script/interpreter.cpp
+++ b/src/script/interpreter.cpp
@@ -93,76 +93,76 @@ bool static IsCompressedOrUncompressedPubKey(const valtype &vchPubKey) {
  * in which case a single 0 byte is necessary and even required).
  * 
  * See https://bitcointalk.org/index.php?topic=8392.msg127623#msg127623
+ *
+ * This function is consensus-critical since BIP66.
  */
-bool static IsDERSignature(const valtype &vchSig) {
+bool static IsValidSignatureEncoding(const std::vector<unsigned char> &sig) {
+    // Format: 0x30 [total-length] 0x02 [R-length] [R] 0x02 [S-length] [S] [sighash]
+    // * total-length: 1-byte length descriptor of everything that follows,
+    //   excluding the sighash byte.
+    // * R-length: 1-byte length descriptor of the R value that follows.
+    // * R: arbitrary-length big-endian encoded R value. It must use the shortest
+    //   possible encoding for a positive integers (which means no null bytes at
+    //   the start, except a single one when the next byte has its highest bit set).
+    // * S-length: 1-byte length descriptor of the S value that follows.
+    // * S: arbitrary-length big-endian encoded S value. The same rules apply.
+    // * sighash: 1-byte value indicating what data is hashed (not part of the DER
+    //   signature)
 
-    if (vchSig.size() < 9) {
-        //  Non-canonical signature: too short
-        return false;
-    }
-    if (vchSig.size() > 73) {
-        // Non-canonical signature: too long
-        return false;
-    }
-    if (vchSig[0] != 0x30) {
-        //  Non-canonical signature: wrong type
-        return false;
-    }
-    if (vchSig[1] != vchSig.size()-3) {
-        //  Non-canonical signature: wrong length marker
-        return false;
-    }
-    unsigned int nLenR = vchSig[3];
-    if (5 + nLenR >= vchSig.size()) {
-        //  Non-canonical signature: S length misplaced
-        return false;
-    }
-    unsigned int nLenS = vchSig[5+nLenR];
-    if ((unsigned long)(nLenR+nLenS+7) != vchSig.size()) {
-        //  Non-canonical signature: R+S length mismatch
-        return false;
-    }
+    // Minimum and maximum size constraints.
+    if (sig.size() < 9) return false;
+    if (sig.size() > 73) return false;
 
-    const unsigned char *R = &vchSig[4];
-    if (R[-2] != 0x02) {
-        //  Non-canonical signature: R value type mismatch
-        return false;
-    }
-    if (nLenR == 0) {
-        //  Non-canonical signature: R length is zero
-        return false;
-    }
-    if (R[0] & 0x80) {
-        //  Non-canonical signature: R value negative
-        return false;
-    }
-    if (nLenR > 1 && (R[0] == 0x00) && !(R[1] & 0x80)) {
-        //  Non-canonical signature: R value excessively padded
-        return false;
-    }
+    // A signature is of type 0x30 (compound).
+    if (sig[0] != 0x30) return false;
+
+    // Make sure the length covers the entire signature.
+    if (sig[1] != sig.size() - 3) return false;
+
+    // Extract the length of the R element.
+    unsigned int lenR = sig[3];
+
+    // Make sure the length of the S element is still inside the signature.
+    if (5 + lenR >= sig.size()) return false;
+
+    // Extract the length of the S element.
+    unsigned int lenS = sig[5 + lenR];
+
+    // Verify that the length of the signature matches the sum of the length
+    // of the elements.
+    if ((size_t)(lenR + lenS + 7) != sig.size()) return false;
+ 
+    // Check whether the R element is an integer.
+    if (sig[2] != 0x02) return false;
+
+    // Zero-length integers are not allowed for R.
+    if (lenR == 0) return false;
+
+    // Negative numbers are not allowed for R.
+    if (sig[4] & 0x80) return false;
+
+    // Null bytes at the start of R are not allowed, unless R would
+    // otherwise be interpreted as a negative number.
+    if (lenR > 1 && (sig[4] == 0x00) && !(sig[5] & 0x80)) return false;
+
+    // Check whether the S element is an integer.
+    if (sig[lenR + 4] != 0x02) return false;
+
+    // Zero-length integers are not allowed for S.
+    if (lenS == 0) return false;
+
+    // Negative numbers are not allowed for S.
+    if (sig[lenR + 6] & 0x80) return false;
+
+    // Null bytes at the start of S are not allowed, unless S would otherwise be
+    // interpreted as a negative number.
+    if (lenS > 1 && (sig[lenR + 6] == 0x00) && !(sig[lenR + 7] & 0x80)) return false;
 
-    const unsigned char *S = &vchSig[6+nLenR];
-    if (S[-2] != 0x02) {
-        //  Non-canonical signature: S value type mismatch
-        return false;
-    }
-    if (nLenS == 0) {
-        //  Non-canonical signature: S length is zero
-        return false;
-    }
-    if (S[0] & 0x80) {
-        //  Non-canonical signature: S value negative
-        return false;
-    }
-    if (nLenS > 1 && (S[0] == 0x00) && !(S[1] & 0x80)) {
-        //  Non-canonical signature: S value excessively padded
-        return false;
-    }
     return true;
 }
 
 bool static IsLowDERSignature(const valtype &vchSig, ScriptError* serror) {
-    if (!IsDERSignature(vchSig)) {
+    if (!IsValidSignatureEncoding(vchSig)) {
         return set_error(serror, SCRIPT_ERR_SIG_DER);
     }
     unsigned int nLenR = vchSig[3];
@@ -194,7 +194,7 @@ bool static CheckSignatureEncoding(const valtype &vchSig, unsigned int flags, Sc
     if (vchSig.size() == 0) {
         return true;
     }
-    if ((flags & (SCRIPT_VERIFY_DERSIG | SCRIPT_VERIFY_LOW_S | SCRIPT_VERIFY_STRICTENC)) != 0 && !IsDERSignature(vchSig)) {
+    if ((flags & (SCRIPT_VERIFY_DERSIG | SCRIPT_VERIFY_LOW_S | SCRIPT_VERIFY_STRICTENC)) != 0 && !IsValidSignatureEncoding(vchSig)) {
         return set_error(serror, SCRIPT_ERR_SIG_DER);
     } else if ((flags & SCRIPT_VERIFY_LOW_S) != 0 && !IsLowDERSignature(vchSig, serror)) {
         // serror is set