diff --git a/src/script/script.h b/src/script/script.h
index e97967dcea..05f2e7e3a9 100644
--- a/src/script/script.h
+++ b/src/script/script.h
@@ -197,8 +197,23 @@ public:
         if (vch.size() > nMaxNumSize) {
             throw scriptnum_error("script number overflow");
         }
-        if (fRequireMinimal && vch.size() > 0 && (vch.back() & 0x7f) == 0 && (vch.size() <= 1 || (vch[vch.size() - 2] & 0x80) == 0)) {
-            throw scriptnum_error("non-minimally encoded script number");
+        if (fRequireMinimal && vch.size() > 0) {
+            // Check that the number is encoded with the minimum possible
+            // number of bytes.
+            //
+            // If the most-significant-byte - excluding the sign bit - is zero
+            // then we're not minimal. Note how this test also rejects the
+            // negative-zero encoding, 0x80.
+            if ((vch.back() & 0x7f) == 0) {
+                // One exception: if there's more than one byte and the most
+                // significant bit of the second-most-significant-byte is set
+                // it would conflict with the sign bit. An example of this case
+                // is +-255, which encode to 0xff00 and 0xff80 respectively.
+                // (big-endian).
+                if (vch.size() <= 1 || (vch[vch.size() - 2] & 0x80) == 0) {
+                    throw scriptnum_error("non-minimally encoded script number");
+                }
+            }
         }
         m_value = set_vch(vch);
     }