diff --git a/core/bn.js b/core/bn.js
index 3d5acc5a..52eb23e8 100644
--- a/core/bn.js
+++ b/core/bn.js
@@ -140,7 +140,7 @@ sjcl.bn.prototype = {
       l[i] = (tmp+carry)>>1;
       carry = (tmp&1) << r;
     }
-    if (!l[l.length-1]) {
+    if (!l[l.length-1] && l.length > 1) {
       l.pop();
     }
     return this;
@@ -386,6 +386,7 @@ sjcl.bn.prototype = {
     var montIn = function(c) { return montMul(c, R2); },
     montMul = function(a, b) {
       // Standard Montgomery reduction
+      // Assumes a and b are already mod N
       var k, ab, right, abBar, mask = (1 << (s + 1)) - 1;
 
       ab = a.mul(b);
@@ -419,7 +420,8 @@ sjcl.bn.prototype = {
     },
     montOut = function(c) { return montMul(c, 1); };
 
-    pow = montIn(pow);
+    // pow may be larger than N, and montIn/montMul assume their params are already mod N.
+    pow = montIn(pow.mod(N));
     out = montIn(out);
 
     // Sliding-Window Exponentiation (HAC 14.85)
diff --git a/test/bn_test.js b/test/bn_test.js
index 37ec13f5..b03f8ea9 100644
--- a/test/bn_test.js
+++ b/test/bn_test.js
@@ -95,3 +95,21 @@ new sjcl.test.TestCase("Big Limbs Multiplication test", function (cb) {
 
   cb && cb();
 });
+
+
+new sjcl.test.TestCase("Regression: Halving one makes zero", function (cb) {
+  if (!sjcl.bn) {
+    this.unimplemented();
+    cb && cb();
+    return;
+  }
+
+  var actual = new sjcl.bn(1).halveM();
+  this.require(actual.limbs.length === 1, "Expected: " + [0] + " Actual: " + actual.limbs);
+  this.require(actual.limbs[0] === 0, "Expected: " + [0] + " Actual: " + actual.limbs);
+
+  actual = new sjcl.bn(0).halveM();
+  this.require(actual.limbs.length === 1, "Expected: " + [0] + " Actual: " + actual.limbs);
+  this.require(actual.limbs[0] === 0, "Expected: " + [0] + " Actual: " + actual.limbs);
+  cb && cb();
+});
diff --git a/test/bn_vectors.js b/test/bn_vectors.js
index 6d18d51e..16687dfd 100644
--- a/test/bn_vectors.js
+++ b/test/bn_vectors.js
@@ -78,5 +78,11 @@ sjcl.test.vector.bn_powermod = [
     x: "eeaf0ab9adb3008dd6c314c9c25600057674df692c0006e0d5d8e2050b98be48e4",
     N: "b48130d6e07674df740e1d33b4816e0d5d8e20e2050b98be48e457674df74096ea",
     v: "9c3219b694befb9caac51a13eb1ac7053b02c654b6a0541cfa60c483592d478630"
+  },
+  {
+    g: 2000,
+    x: 2,
+    N: 19,
+    v: 6
   }
 ];