diff --git a/src/base/construction.rs b/src/base/construction.rs
index b606534c..2fd0bb7f 100644
--- a/src/base/construction.rs
+++ b/src/base/construction.rs
@@ -284,7 +284,8 @@ where
     where
         Standard: Distribution<N>,
     {
-        Self::from_fn_generic(nrows, ncols, |_, _| rand::random())
+        let mut rng = rand::thread_rng();
+        Self::from_fn_generic(nrows, ncols, |_, _| rng.gen())
     }
 
     /// Creates a matrix filled with random values from the given distribution.
@@ -852,6 +853,7 @@ where
     }
 }
 
+// TODO(specialization): faster impls possible for D≤4 (see rand_distr::{UnitCircle, UnitSphere})
 #[cfg(feature = "rand")]
 impl<N: crate::RealField, D: DimName> Distribution<Unit<VectorN<N, D>>> for Standard
 where
diff --git a/src/geometry/orthographic.rs b/src/geometry/orthographic.rs
index 7b137641..43bf45c6 100644
--- a/src/geometry/orthographic.rs
+++ b/src/geometry/orthographic.rs
@@ -691,6 +691,7 @@ impl<N: RealField> Distribution<Orthographic3<N>> for Standard
 where
     Standard: Distribution<N>,
 {
+    /// Generate an arbitrary random variate for testing purposes.
     fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> Orthographic3<N> {
         use crate::base::helper;
         let left = r.gen();
diff --git a/src/geometry/perspective.rs b/src/geometry/perspective.rs
index 69233952..64861fbd 100644
--- a/src/geometry/perspective.rs
+++ b/src/geometry/perspective.rs
@@ -275,6 +275,7 @@ impl<N: RealField> Distribution<Perspective3<N>> for Standard
 where
     Standard: Distribution<N>,
 {
+    /// Generate an arbitrary random variate for testing purposes.
     fn sample<'a, R: Rng + ?Sized>(&self, r: &'a mut R) -> Perspective3<N> {
         use crate::base::helper;
         let znear = r.gen();
diff --git a/src/geometry/point_construction.rs b/src/geometry/point_construction.rs
index bf88ece0..47b336f4 100644
--- a/src/geometry/point_construction.rs
+++ b/src/geometry/point_construction.rs
@@ -164,6 +164,7 @@ where
     DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
+     /// Generate a `Point` where each coordinate is an independent variate from `[0, 1)`.
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Point<N, D> {
         Point::from(rng.gen::<VectorN<N, D>>())
diff --git a/src/geometry/quaternion_construction.rs b/src/geometry/quaternion_construction.rs
index 50807907..1b87dba0 100644
--- a/src/geometry/quaternion_construction.rs
+++ b/src/geometry/quaternion_construction.rs
@@ -7,7 +7,7 @@ use quickcheck::{Arbitrary, Gen};
 
 #[cfg(feature = "rand-no-std")]
 use rand::{
-    distributions::{Distribution, OpenClosed01, Standard},
+    distributions::{Distribution, OpenClosed01, Standard, Uniform, uniform::SampleUniform},
     Rng,
 };
 
@@ -855,6 +855,7 @@ impl<N: SimdRealField> Distribution<UnitQuaternion<N>> for Standard
 where
     N::Element: SimdRealField,
     OpenClosed01: Distribution<N>,
+    N: SampleUniform,
 {
     /// Generate a uniformly distributed random rotation quaternion.
     #[inline]
@@ -863,10 +864,9 @@ where
         // Uniform random rotations.
         // In D. Kirk, editor, Graphics Gems III, pages 124-132. Academic, New York, 1992.
         let x0 = rng.sample(OpenClosed01);
-        let x1 = rng.sample(OpenClosed01);
-        let x2 = rng.sample(OpenClosed01);
-        let theta1 = N::simd_two_pi() * x1;
-        let theta2 = N::simd_two_pi() * x2;
+        let twopi = Uniform::new(N::zero(), N::simd_two_pi());
+        let theta1 = rng.sample(&twopi);
+        let theta2 = rng.sample(&twopi);
         let s1 = theta1.simd_sin();
         let c1 = theta1.simd_cos();
         let s2 = theta2.simd_sin();
diff --git a/src/geometry/rotation_specialization.rs b/src/geometry/rotation_specialization.rs
index 95e19da1..fe431804 100644
--- a/src/geometry/rotation_specialization.rs
+++ b/src/geometry/rotation_specialization.rs
@@ -7,7 +7,7 @@ use num::Zero;
 
 #[cfg(feature = "rand-no-std")]
 use rand::{
-    distributions::{Distribution, OpenClosed01, Standard},
+    distributions::{Distribution, OpenClosed01, Standard, Uniform, uniform::SampleUniform},
     Rng,
 };
 
@@ -265,12 +265,13 @@ impl<N: SimdRealField> Rotation2<N> {
 impl<N: SimdRealField> Distribution<Rotation2<N>> for Standard
 where
     N::Element: SimdRealField,
-    OpenClosed01: Distribution<N>,
+    N: SampleUniform,
 {
     /// Generate a uniformly distributed random rotation.
     #[inline]
     fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> Rotation2<N> {
-        Rotation2::new(rng.sample(OpenClosed01) * N::simd_two_pi())
+        let twopi = Uniform::new(N::zero(), N::simd_two_pi());
+        Rotation2::new(rng.sample(twopi))
     }
 }
 
@@ -923,6 +924,7 @@ impl<N: SimdRealField> Distribution<Rotation3<N>> for Standard
 where
     N::Element: SimdRealField,
     OpenClosed01: Distribution<N>,
+    N: SampleUniform,
 {
     /// Generate a uniformly distributed random rotation.
     #[inline]
@@ -932,7 +934,8 @@ where
         // In D. Kirk, editor, Graphics Gems III, pages 117-120. Academic, New York, 1992.
 
         // Compute a random rotation around Z
-        let theta = N::simd_two_pi() * rng.sample(OpenClosed01);
+        let twopi = Uniform::new(N::zero(), N::simd_two_pi());
+        let theta = rng.sample(&twopi);
         let (ts, tc) = theta.simd_sin_cos();
         let a = MatrixN::<N, U3>::new(
             tc,
@@ -947,7 +950,7 @@ where
         );
 
         // Compute a random rotation *of* Z
-        let phi = N::simd_two_pi() * rng.sample(OpenClosed01);
+        let phi = rng.sample(&twopi);
         let z = rng.sample(OpenClosed01);
         let (ps, pc) = phi.simd_sin_cos();
         let sqrt_z = z.simd_sqrt();
diff --git a/src/geometry/similarity_construction.rs b/src/geometry/similarity_construction.rs
index 4501bdb7..0c814534 100644
--- a/src/geometry/similarity_construction.rs
+++ b/src/geometry/similarity_construction.rs
@@ -69,6 +69,7 @@ where
     DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N> + Distribution<R>,
 {
+    /// Generate an arbitrary random variate for testing purposes.
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, D, R> {
         let mut s = rng.gen();
diff --git a/src/geometry/translation_construction.rs b/src/geometry/translation_construction.rs
index 964cd105..c1c02862 100644
--- a/src/geometry/translation_construction.rs
+++ b/src/geometry/translation_construction.rs
@@ -78,6 +78,7 @@ where
     DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N>,
 {
+    /// Generate an arbitrary random variate for testing purposes.
     #[inline]
     fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Translation<N, D> {
         Translation::from(rng.gen::<VectorN<N, D>>())
diff --git a/src/geometry/unit_complex_construction.rs b/src/geometry/unit_complex_construction.rs
index 9a24a57d..9f300f3d 100644
--- a/src/geometry/unit_complex_construction.rs
+++ b/src/geometry/unit_complex_construction.rs
@@ -2,10 +2,7 @@
 use quickcheck::{Arbitrary, Gen};
 
 #[cfg(feature = "rand-no-std")]
-use rand::{
-    distributions::{Distribution, OpenClosed01, Standard},
-    Rng,
-};
+use rand::{distributions::{Distribution, Standard}, Rng};
 
 use num::One;
 use num_complex::Complex;
@@ -401,12 +398,13 @@ where
 impl<N: SimdRealField> Distribution<UnitComplex<N>> for Standard
 where
     N::Element: SimdRealField,
-    OpenClosed01: Distribution<N>,
+    rand_distr::UnitCircle: Distribution<[N; 2]>,
 {
     /// Generate a uniformly distributed random `UnitComplex`.
     #[inline]
     fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> UnitComplex<N> {
-        UnitComplex::from_angle(rng.sample(OpenClosed01) * N::simd_two_pi())
+        let x = rng.sample(rand_distr::UnitCircle);
+        UnitComplex::new_unchecked(Complex::new(x[0], x[1]))
     }
 }
 
diff --git a/tests/core/helper.rs b/tests/core/helper.rs
index ef749da6..ec214fc0 100644
--- a/tests/core/helper.rs
+++ b/tests/core/helper.rs
@@ -33,6 +33,8 @@ where
 
 // This is a wrapper similar to RandComplex, but for non-complex.
 // This exists only to make generic tests easier to write.
+//
+// Generates variates in the range [0, 1).
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
 pub struct RandScalar<N>(pub N);