diff --git a/src/prng/chacha.rs b/src/prng/chacha.rs
index db1d127bb9c..a9ae8996b09 100644
--- a/src/prng/chacha.rs
+++ b/src/prng/chacha.rs
@@ -235,7 +235,7 @@ impl Rng for ChaChaRng {
             unsafe{ copy_nonoverlapping(
                 &self.buffer[self.index].0 as *const u32 as *const u8,
                 l.as_mut_ptr(),
-                words) };
+                4 * words) };
             self.index += words;
         }
         let n = left.len();
@@ -351,6 +351,20 @@ mod test {
                         0x2c5bad8f, 0x898881dc, 0x5f1c86d9, 0xc1f8e7f4));
     }
 
+    #[test]
+    fn test_rng_true_bytes() {
+        let seed : &[_] = &[0u32; 8];
+        let mut ra: ChaChaRng = SeedableRng::from_seed(seed);
+        let mut buf = [0u8; 32];
+        ra.fill_bytes(&mut buf);
+        // Same as first values in test_isaac_true_values as bytes in LE order
+        assert_eq!(buf,
+                   [118, 184, 224, 173, 160, 241, 61, 144,
+                    64, 93, 106, 229, 83, 134, 189, 40,
+                    189, 210, 25, 184, 160, 141, 237, 26,
+                    168, 54, 239, 204, 139, 119, 13, 199]);
+    }
+    
     #[test]
     fn test_rng_clone() {
         let seed : &[_] = &[0u32; 8];
diff --git a/src/prng/isaac.rs b/src/prng/isaac.rs
index 996bc684f5b..82944144cb8 100644
--- a/src/prng/isaac.rs
+++ b/src/prng/isaac.rs
@@ -407,6 +407,20 @@ mod test {
                         141456972, 2478885421));
     }
 
+    #[test]
+    fn test_isaac_true_bytes() {
+        let seed: &[_] = &[1, 23, 456, 7890, 12345];
+        let mut rng1 = IsaacRng::from_seed(seed);
+        let mut buf = [0u8; 32];
+        rng1.fill_bytes(&mut buf);
+        // Same as first values in test_isaac_true_values as bytes in LE order
+        assert_eq!(buf,
+                   [82, 186, 128, 152, 71, 240, 20, 52,
+                    45, 175, 180, 15, 86, 16, 99, 125,
+                    101, 203, 81, 214, 97, 162, 134, 250,
+                    103, 78, 203, 15, 150, 3, 210, 164]);
+    }
+    
     #[test]
     fn test_isaac_new_uninitialized() {
         // Compare the results from initializing `IsaacRng` with
diff --git a/src/prng/isaac64.rs b/src/prng/isaac64.rs
index 91c0186f3c7..1d84d555f72 100644
--- a/src/prng/isaac64.rs
+++ b/src/prng/isaac64.rs
@@ -219,7 +219,7 @@ impl Rng for Isaac64Rng {
     }
 
     fn fill_bytes(&mut self, dest: &mut [u8]) {
-        ::rand_core::impls::fill_bytes_via_u32(self, dest);
+        ::rand_core::impls::fill_bytes_via_u64(self, dest);
     }
 
     fn try_fill(&mut self, dest: &mut [u8]) -> Result<(), Error> {
@@ -370,7 +370,21 @@ mod test {
                         596345674630742204, 9947027391921273664,
                         11788097613744130851, 10391409374914919106));
     }
-
+    
+    #[test]
+    fn test_isaac64_true_bytes() {
+        let seed: &[_] = &[1, 23, 456, 7890, 12345];
+        let mut rng1 = Isaac64Rng::from_seed(seed);
+        let mut buf = [0u8; 32];
+        rng1.fill_bytes(&mut buf);
+        // Same as first values in test_isaac64_true_values as bytes in LE order
+        assert_eq!(buf,
+                   [140, 237, 103, 8, 93, 196, 151, 7,
+                    156, 242, 26, 63, 54, 166, 135, 199,
+                    141, 186, 192, 50, 116, 69, 205, 240,
+                    98, 205, 127, 160, 83, 98, 49, 17]);
+    }
+    
     #[test]
     fn test_isaac_new_uninitialized() {
         // Compare the results from initializing `IsaacRng` with