diff --git a/lib/uuid.js b/lib/uuid.js
index f616d52..1963639 100644
--- a/lib/uuid.js
+++ b/lib/uuid.js
@@ -21,26 +21,33 @@ UUIDjs.limitUI32 = UUIDjs.maxFromBits(32);
 UUIDjs.limitUI40 = UUIDjs.maxFromBits(40);
 UUIDjs.limitUI48 = UUIDjs.maxFromBits(48);
 
+// Returns a random integer between min and max
+// Using Math.round() will give you a non-uniform distribution!
+// @see https://developer.mozilla.org/en-US/docs/JavaScript/Reference/Global_Objects/Math/random
+function getRandomInt(min, max) {
+  return Math.floor(Math.random() * (max - min + 1)) + min;
+}
+
 UUIDjs.randomUI04 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI04);
+  return getRandomInt(0, UUIDjs.limitUI04-1);
 };
 UUIDjs.randomUI06 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI06);
+  return getRandomInt(0, UUIDjs.limitUI06-1);
 };
 UUIDjs.randomUI08 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI08);
+  return getRandomInt(0, UUIDjs.limitUI08-1);
 };
 UUIDjs.randomUI12 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI12);
+  return getRandomInt(0, UUIDjs.limitUI12-1);
 };
 UUIDjs.randomUI14 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI14);
+  return getRandomInt(0, UUIDjs.limitUI14-1);
 };
 UUIDjs.randomUI16 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI16);
+  return getRandomInt(0, UUIDjs.limitUI16-1);
 };
 UUIDjs.randomUI32 = function() {
-  return Math.round(Math.random() * UUIDjs.limitUI32);
+  return getRandomInt(0, UUIDjs.limitUI32-1);
 };
 UUIDjs.randomUI40 = function() {
   return (0 | Math.random() * (1 << 30)) + (0 | Math.random() * (1 << 40 - 30)) * (1 << 30);
diff --git a/test/uuid.js b/test/uuid.js
index c028d70..c37527e 100644
--- a/test/uuid.js
+++ b/test/uuid.js
@@ -329,6 +329,25 @@ exports['newTS() alias for create(1)'] = function() {
   spy.restore();
 };
 
+exports['correct random max values'] = function() {
+
+  var stub = sinon.stub(Math, 'random').returns(0.9999999999);
+
+  assert.equal(UUID.randomUI04(), 0x0000000F);
+  assert.equal(UUID.randomUI06(), 0x0000003F);
+  assert.equal(UUID.randomUI08(), 0x000000FF);
+  assert.equal(UUID.randomUI12(), 0x00000FFF);
+  assert.equal(UUID.randomUI14(), 0x00003FFF);
+  assert.equal(UUID.randomUI16(), 0x0000FFFF);
+  assert.equal(UUID.randomUI32(), 0xFFFFFFFF);
+
+  // not really sure about these....
+  assert.equal(UUID.randomUI40(), 0xFFFFFFFFFF);
+  assert.equal(UUID.randomUI48(), 0xFFFFFFFFFFFF);
+
+  stub.restore();
+
+};
 
 for (var key in exports) {
   exports[key]();