diff --git a/src/int/rand.rs b/src/int/rand.rs
index 94f02e61..07a194b7 100644
--- a/src/int/rand.rs
+++ b/src/int/rand.rs
@@ -1,6 +1,6 @@
 //! Random number generator support
 
-use rand_core::{RngCore, TryRngCore};
+use rand_core::TryRngCore;
 
 use crate::{Int, Random, RandomBits, RandomBitsError};
 
@@ -8,8 +8,8 @@ use super::Uint;
 
 impl<const LIMBS: usize> Random for Int<LIMBS> {
     /// Generate a cryptographically secure random [`Int`].
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        Self(Uint::random(rng))
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
+        Ok(Self(Uint::try_random(rng)?))
     }
 }
 
diff --git a/src/limb/rand.rs b/src/limb/rand.rs
index 2a5ba16c..22fd4218 100644
--- a/src/limb/rand.rs
+++ b/src/limb/rand.rs
@@ -2,18 +2,17 @@
 
 use super::Limb;
 use crate::{Encoding, NonZero, Random, RandomMod};
-use rand_core::{RngCore, TryRngCore};
+use rand_core::TryRngCore;
 use subtle::ConstantTimeLess;
 
 impl Random for Limb {
-    #[cfg(target_pointer_width = "32")]
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        Self(rng.next_u32())
-    }
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
+        #[cfg(target_pointer_width = "32")]
+        let val = rng.try_next_u32()?;
+        #[cfg(target_pointer_width = "64")]
+        let val = rng.try_next_u64()?;
 
-    #[cfg(target_pointer_width = "64")]
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        Self(rng.next_u64())
+        Ok(Self(val))
     }
 }
 
diff --git a/src/modular/const_monty_form.rs b/src/modular/const_monty_form.rs
index 8ff8dd80..cfd2511c 100644
--- a/src/modular/const_monty_form.rs
+++ b/src/modular/const_monty_form.rs
@@ -15,7 +15,7 @@ use core::{fmt::Debug, marker::PhantomData};
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
 
 #[cfg(feature = "rand_core")]
-use crate::{Random, RandomMod, rand_core::RngCore};
+use crate::{Random, RandomMod, rand_core::TryRngCore};
 
 #[cfg(feature = "serde")]
 use {
@@ -204,8 +204,11 @@ where
     MOD: ConstMontyParams<LIMBS>,
 {
     #[inline]
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        Self::new(&Uint::random_mod(rng, MOD::MODULUS.as_nz_ref()))
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
+        Ok(Self::new(&Uint::try_random_mod(
+            rng,
+            MOD::MODULUS.as_nz_ref(),
+        )?))
     }
 }
 
diff --git a/src/non_zero.rs b/src/non_zero.rs
index 741c66e2..e76b5b97 100644
--- a/src/non_zero.rs
+++ b/src/non_zero.rs
@@ -12,7 +12,7 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 use crate::{ArrayEncoding, ByteArray};
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::RngCore};
+use {crate::Random, rand_core::TryRngCore};
 
 #[cfg(feature = "serde")]
 use serdect::serde::{
@@ -246,10 +246,10 @@ where
     /// As a result, it runs in variable time. If the generator `rng` is
     /// cryptographically secure (for example, it implements `CryptoRng`),
     /// then this is guaranteed not to leak anything about the output value.
-    fn random<R: RngCore + ?Sized>(mut rng: &mut R) -> Self {
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
         loop {
-            if let Some(result) = Self::new(T::random(&mut rng)).into() {
-                break result;
+            if let Some(result) = Self::new(T::try_random(rng)?).into() {
+                break Ok(result);
             }
         }
     }
diff --git a/src/odd.rs b/src/odd.rs
index 4f076211..b442a632 100644
--- a/src/odd.rs
+++ b/src/odd.rs
@@ -8,10 +8,10 @@ use subtle::{Choice, ConditionallySelectable, ConstantTimeEq, CtOption};
 use crate::BoxedUint;
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::RngCore};
+use crate::{Random, rand_core::TryRngCore};
 
 #[cfg(all(feature = "alloc", feature = "rand_core"))]
-use {crate::RandomBits, rand_core::TryRngCore};
+use crate::RandomBits;
 
 #[cfg(feature = "serde")]
 use crate::Zero;
@@ -153,10 +153,10 @@ impl PartialOrd<Odd<BoxedUint>> for BoxedUint {
 #[cfg(feature = "rand_core")]
 impl<const LIMBS: usize> Random for Odd<Uint<LIMBS>> {
     /// Generate a random `Odd<Uint<T>>`.
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        let mut ret = Uint::random(rng);
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
+        let mut ret = Uint::try_random(rng)?;
         ret.limbs[0] |= Limb::ONE;
-        Odd(ret)
+        Ok(Odd(ret))
     }
 }
 
diff --git a/src/traits.rs b/src/traits.rs
index 86079823..962b6f52 100644
--- a/src/traits.rs
+++ b/src/traits.rs
@@ -299,7 +299,15 @@ pub trait Random: Sized {
     /// Generate a random value.
     ///
     /// If `rng` is a CSRNG, the generation is cryptographically secure as well.
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self;
+    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
+        let Ok(out) = Self::try_random(rng);
+        out
+    }
+
+    /// Generate a random value.
+    ///
+    /// If `rng` is a CSRNG, the generation is cryptographically secure as well.
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error>;
 }
 
 /// Possible errors of the methods in [`RandomBits`] trait.
diff --git a/src/uint/rand.rs b/src/uint/rand.rs
index 98d954ba..b37021c1 100644
--- a/src/uint/rand.rs
+++ b/src/uint/rand.rs
@@ -6,14 +6,14 @@ use rand_core::{RngCore, TryRngCore};
 use subtle::ConstantTimeLess;
 
 impl<const LIMBS: usize> Random for Uint<LIMBS> {
-    fn random<R: RngCore + ?Sized>(mut rng: &mut R) -> Self {
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
         let mut limbs = [Limb::ZERO; LIMBS];
 
         for limb in &mut limbs {
-            *limb = Limb::random(&mut rng)
+            *limb = Limb::try_random(rng)?
         }
 
-        limbs.into()
+        Ok(limbs.into())
     }
 }
 
diff --git a/src/wrapping.rs b/src/wrapping.rs
index 414eaa22..3b2b969d 100644
--- a/src/wrapping.rs
+++ b/src/wrapping.rs
@@ -8,7 +8,7 @@ use core::{
 use subtle::{Choice, ConditionallySelectable, ConstantTimeEq};
 
 #[cfg(feature = "rand_core")]
-use {crate::Random, rand_core::RngCore};
+use {crate::Random, rand_core::TryRngCore};
 
 #[cfg(feature = "serde")]
 use serdect::serde::{Deserialize, Deserializer, Serialize, Serializer};
@@ -259,8 +259,8 @@ impl<T: fmt::UpperHex> fmt::UpperHex for Wrapping<T> {
 
 #[cfg(feature = "rand_core")]
 impl<T: Random> Random for Wrapping<T> {
-    fn random<R: RngCore + ?Sized>(rng: &mut R) -> Self {
-        Wrapping(Random::random(rng))
+    fn try_random<R: TryRngCore + ?Sized>(rng: &mut R) -> Result<Self, R::Error> {
+        Ok(Wrapping(Random::try_random(rng)?))
     }
 }