diff --git a/verinum.cc b/verinum.cc
index 84debdb1b..a463cdb63 100644
--- a/verinum.cc
+++ b/verinum.cc
@@ -997,9 +997,9 @@ verinum::V operator & (verinum::V l, verinum::V r)
 verinum::V operator ^ (verinum::V l, verinum::V r)
 {
       if (l == verinum::V0)
-	    return r;
+	    return bit4_z2x(r);
       if (r == verinum::V0)
-	    return l;
+	    return bit4_z2x(l);
       if ((l == verinum::V1) && (r == verinum::V1))
 	    return verinum::V0;
 
diff --git a/verinum.h b/verinum.h
index aa92206b0..39caae4e8 100644
--- a/verinum.h
+++ b/verinum.h
@@ -113,6 +113,9 @@ extern verinum trim_vnum(const verinum&);
 extern std::ostream& operator<< (std::ostream&, const verinum&);
 extern std::ostream& operator<< (std::ostream&, verinum::V);
 
+inline verinum::V bit4_z2x(verinum::V bit)
+{ return bit<2? bit : verinum::Vx; /* Relies on V0 and V1 being <2 */}
+
 extern verinum::V operator ~ (verinum::V l);
 extern verinum::V operator | (verinum::V l, verinum::V r);
 extern verinum::V operator & (verinum::V l, verinum::V r);