diff --git a/src/key.cpp b/src/key.cpp
index b57b7c506..2199996cf 100644
--- a/src/key.cpp
+++ b/src/key.cpp
@@ -332,30 +332,60 @@ public:
     }
 };
 
+int CompareBigEndian(const unsigned char *c1, size_t c1len, const unsigned char *c2, size_t c2len) {
+    while (c1len > c2len) {
+        if (*c1)
+            return 1;
+        c1++;
+        c1len--;
+    }
+    while (c2len > c1len) {
+        if (*c2)
+            return -1;
+        c2++;
+        c2len--;
+    }
+    while (c1len > 0) {
+        if (*c1 > *c2)
+            return 1;
+        if (*c2 > *c1)
+            return -1;
+        c1++;
+        c2++;
+        c1len--;
+    }
+    return 0;
+}
+
+// Order of secp256k1's generator minus 1.
+const unsigned char vchMaxModOrder[32] = {
+    0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+    0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
+    0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+    0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
+};
+
+// Half of the order of secp256k1's generator minus 1.
+const unsigned char vchMaxModHalfOrder[32] = {
+    0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+    0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+    0x5D,0x57,0x6E,0x73,0x57,0xA4,0x50,0x1D,
+    0xDF,0xE9,0x2F,0x46,0x68,0x1B,0x20,0xA0
+};
+
+const unsigned char vchZero[0] = {};
+
+
 }; // end of anonymous namespace
 
 bool CKey::Check(const unsigned char *vch) {
-    // Do not convert to OpenSSL's data structures for range-checking keys,
-    // it's easy enough to do directly.
-    static const unsigned char vchMax[32] = {
-        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
-        0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
-        0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
-        0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x40
-    };
-    bool fIsZero = true;
-    for (int i=0; i<32 && fIsZero; i++)
-        if (vch[i] != 0)
-            fIsZero = false;
-    if (fIsZero)
-        return false;
-    for (int i=0; i<32; i++) {
-        if (vch[i] < vchMax[i])
-            return true;
-        if (vch[i] > vchMax[i])
-            return false;
-    }
-    return true;
+    return CompareBigEndian(vch, 32, vchZero, 0) > 0 &&
+           CompareBigEndian(vch, 32, vchMaxModOrder, 32) <= 0;
+}
+
+bool CKey::CheckSignatureElement(const unsigned char *vch, int len, bool half) {
+    return CompareBigEndian(vch, len, vchZero, 0) > 0 &&
+           CompareBigEndian(vch, len, half ? vchMaxModHalfOrder : vchMaxModOrder, 32) <= 0;
 }
 
 void CKey::MakeNewKey(bool fCompressedIn) {
diff --git a/src/key.h b/src/key.h
index cf1165d3d..37a06810b 100644
--- a/src/key.h
+++ b/src/key.h
@@ -269,6 +269,9 @@ public:
 
     // Load private key and check that public key matches.
     bool Load(CPrivKey &privkey, CPubKey &vchPubKey, bool fSkipCheck);
+
+    // Check whether an element of a signature (r or s) is valid.
+    static bool CheckSignatureElement(const unsigned char *vch, int len, bool half);
 };
 
 struct CExtPubKey {
diff --git a/src/script.cpp b/src/script.cpp
index 810ba16d2..84a2a629e 100644
--- a/src/script.cpp
+++ b/src/script.cpp
@@ -296,9 +296,12 @@ bool IsCanonicalSignature(const valtype &vchSig, unsigned int flags) {
     if (nLenS > 1 && (S[0] == 0x00) && !(S[1] & 0x80))
         return error("Non-canonical signature: S value excessively padded");
 
-    if (flags & SCRIPT_VERIFY_EVEN_S) {
-        if (S[nLenS-1] & 1)
-            return error("Non-canonical signature: S value odd");
+    if (flags & SCRIPT_VERIFY_LOW_S) {
+        // If the S value is above the order of the curve divided by two, its
+        // complement modulo the order could have been used instead, which is
+        // one byte shorter when encoded correctly.
+        if (!CKey::CheckSignatureElement(S, nLenS, true))
+            return error("Non-canonical signature: S value is unnecessarily high");
     }
 
     return true;
diff --git a/src/script.h b/src/script.h
index 657ac0b38..b96bbc45c 100644
--- a/src/script.h
+++ b/src/script.h
@@ -40,7 +40,7 @@ enum
     SCRIPT_VERIFY_NONE      = 0,
     SCRIPT_VERIFY_P2SH      = (1U << 0), // evaluate P2SH (BIP16) subscripts
     SCRIPT_VERIFY_STRICTENC = (1U << 1), // enforce strict conformance to DER and SEC2 for signatures and pubkeys
-    SCRIPT_VERIFY_EVEN_S    = (1U << 2), // enforce even S values in signatures (depends on STRICTENC)
+    SCRIPT_VERIFY_LOW_S     = (1U << 2), // enforce low S values (<n/2) in signatures (depends on STRICTENC)
     SCRIPT_VERIFY_NOCACHE   = (1U << 3), // do not store results in signature cache (but do query it)
 };
 
diff --git a/src/test/canonical_tests.cpp b/src/test/canonical_tests.cpp
index c521f2cf9..c38d9db57 100644
--- a/src/test/canonical_tests.cpp
+++ b/src/test/canonical_tests.cpp
@@ -89,4 +89,21 @@ BOOST_AUTO_TEST_CASE(script_noncanon)
     }
 }
 
+BOOST_AUTO_TEST_CASE(script_signstrict)
+{
+    for (int i=0; i<100; i++) {
+        CKey key;
+        key.MakeNewKey(i & 1);
+        std::vector<unsigned char> sig;
+        uint256 hash = GetRandHash();
+
+        BOOST_CHECK(key.Sign(hash, sig)); // Generate a random signature.
+        BOOST_CHECK(key.GetPubKey().Verify(hash, sig)); // Check it.
+        sig.push_back(0x01); // Append a sighash type.
+
+        BOOST_CHECK(IsCanonicalSignature(sig, SCRIPT_VERIFY_STRICTENC | SCRIPT_VERIFY_LOW_S));
+        BOOST_CHECK(IsCanonicalSignature_OpenSSL(sig));
+    }
+}
+
 BOOST_AUTO_TEST_SUITE_END()