diff --git a/src/bigrand.rs b/src/bigrand.rs
index a163bbf..f67c079 100644
--- a/src/bigrand.rs
+++ b/src/bigrand.rs
@@ -1,6 +1,7 @@
 //! Randomization of big integers
 
 use rand::Rng;
+use rand::distributions::uniform::{SampleUniform, UniformSampler};
 
 use BigInt;
 use BigUint;
@@ -34,8 +35,7 @@ pub trait RandBigInt {
     fn gen_bigint_range(&mut self, lbound: &BigInt, ubound: &BigInt) -> BigInt;
 }
 
-#[cfg(any(feature = "rand", test))]
-impl<R: Rng> RandBigInt for R {
+impl<R: Rng + ?Sized> RandBigInt for R {
     fn gen_biguint(&mut self, bit_size: usize) -> BigUint {
         use super::big_digit::BITS;
         let (digits, rem) = bit_size.div_rem(&BITS);
@@ -106,3 +106,40 @@ impl<R: Rng> RandBigInt for R {
         }
     }
 }
+
+
+/// The back-end implementing rand's `UniformSampler` for `BigUint`.
+#[derive(Clone, Debug)]
+pub struct UniformBigUint {
+    base: BigUint,
+    len: BigUint,
+}
+
+impl UniformSampler for UniformBigUint {
+    type X = BigUint;
+
+    fn new(low: Self::X, high: Self::X) -> Self {
+        assert!(low < high);
+        UniformBigUint {
+            len: high - &low,
+            base: low,
+        }
+    }
+
+    fn new_inclusive(low: Self::X, high: Self::X) -> Self {
+        assert!(low <= high);
+        Self::new(low, high + 1u32)
+    }
+
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Self::X {
+        &self.base + rng.gen_biguint_below(&self.len)
+    }
+
+    fn sample_single<R: Rng + ?Sized>(low: Self::X, high: Self::X, rng: &mut R) -> Self::X {
+        rng.gen_biguint_range(&low, &high)
+    }
+}
+
+impl SampleUniform for BigUint {
+    type Sampler = UniformBigUint;
+}
diff --git a/src/lib.rs b/src/lib.rs
index 6bc15f6..922fcd9 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -163,7 +163,7 @@ pub use bigint::BigInt;
 pub use bigint::ToBigInt;
 
 #[cfg(feature = "rand")]
-pub use bigrand::RandBigInt;
+pub use bigrand::{RandBigInt, UniformBigUint};
 
 mod big_digit {
     /// A `BigDigit` is a `BigUint`'s composing element.
diff --git a/tests/rand.rs b/tests/rand.rs
index 553c263..284fa69 100644
--- a/tests/rand.rs
+++ b/tests/rand.rs
@@ -8,6 +8,8 @@ mod biguint {
     use num_bigint::{BigUint, RandBigInt};
     use num_traits::Zero;
     use rand::thread_rng;
+    use rand::Rng;
+    use rand::distributions::Uniform;
 
     #[test]
     fn test_rand() {
@@ -54,6 +56,29 @@ mod biguint {
         // Switching u and l should fail:
         let _n: BigUint = rng.gen_biguint_range(&u, &l);
     }
+
+    #[test]
+    fn test_rand_uniform() {
+        let mut rng = thread_rng();
+
+        let tiny = Uniform::new(BigUint::from(236u32), BigUint::from(237u32));
+        for _ in 0..10 {
+            assert_eq!(rng.sample(&tiny), BigUint::from(236u32));
+        }
+
+        let l = BigUint::from(403469000u32 + 2352);
+        let u = BigUint::from(403469000u32 + 3513);
+        let below = Uniform::new(BigUint::zero(), u.clone());
+        let range = Uniform::new(l.clone(), u.clone());
+        for _ in 0..1000 {
+            let n: BigUint = rng.sample(&below);
+            assert!(n < u);
+
+            let n: BigUint = rng.sample(&range);
+            assert!(n >= l);
+            assert!(n < u);
+        }
+    }
 }
 
 mod bigint {