diff --git a/CHANGELOG.md b/CHANGELOG.md
index 44603eeb53..32919ded61 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -32,6 +32,7 @@ You may also find the [Upgrade Guide](https://rust-random.github.io/book/update.
 - Rename `Rng::gen_range` to `random_range`, `gen_bool` to `random_bool`, `gen_ratio` to `random_ratio` (#1505)
 - Rename `Standard` to `StandardUniform` (#1526)
 - Remove impl of `Distribution<Option<T>>` for `Standard` (#1526)
+- Remove first parameter (`rng`) of `ReseedingRng::new` (#1533)
 
 ## [0.9.0-alpha.1] - 2024-03-18
 - Add the `Slice::num_choices` method to the Slice distribution (#1402)
diff --git a/benches/benches/generators.rs b/benches/benches/generators.rs
index 95361cd203..5c98d37ef6 100644
--- a/benches/benches/generators.rs
+++ b/benches/benches/generators.rs
@@ -201,7 +201,7 @@ pub fn reseeding_bytes(c: &mut Criterion) {
     fn bench(g: &mut BenchmarkGroup<WallTime>, thresh: u64) {
         let name = format!("chacha20_{}k", thresh);
         g.bench_function(name.as_str(), |b| {
-            let mut rng = ReseedingRng::new(ChaCha20Core::from_os_rng(), thresh * 1024, OsRng);
+            let mut rng = ReseedingRng::<ChaCha20Core, _>::new(thresh * 1024, OsRng).unwrap();
             let mut buf = [0u8; 1024 * 1024];
             b.iter(|| {
                 rng.fill_bytes(&mut buf);
diff --git a/src/rngs/reseeding.rs b/src/rngs/reseeding.rs
index a0076f959a..570d04eeba 100644
--- a/src/rngs/reseeding.rs
+++ b/src/rngs/reseeding.rs
@@ -59,8 +59,7 @@ use rand_core::{CryptoRng, RngCore, SeedableRng, TryCryptoRng, TryRngCore};
 /// use rand::rngs::OsRng;
 /// use rand::rngs::ReseedingRng;
 ///
-/// let prng = ChaCha20Core::from_os_rng();
-/// let mut reseeding_rng = ReseedingRng::new(prng, 0, OsRng);
+/// let mut reseeding_rng = ReseedingRng::<ChaCha20Core, _>::new(0, OsRng).unwrap();
 ///
 /// println!("{}", reseeding_rng.random::<u64>());
 ///
@@ -88,8 +87,10 @@ where
     /// `threshold` sets the number of generated bytes after which to reseed the
     /// PRNG. Set it to zero to never reseed based on the number of generated
     /// values.
-    pub fn new(rng: R, threshold: u64, reseeder: Rsdr) -> Self {
-        ReseedingRng(BlockRng::new(ReseedingCore::new(rng, threshold, reseeder)))
+    pub fn new(threshold: u64, reseeder: Rsdr) -> Result<Self, Rsdr::Error> {
+        Ok(ReseedingRng(BlockRng::new(ReseedingCore::new(
+            threshold, reseeder,
+        )?)))
     }
 
     /// Immediately reseed the generator
@@ -177,7 +178,10 @@ where
     Rsdr: TryRngCore,
 {
     /// Create a new `ReseedingCore`.
-    fn new(rng: R, threshold: u64, reseeder: Rsdr) -> Self {
+    ///
+    /// `threshold` is the maximum number of bytes produced by
+    /// [`BlockRngCore::generate`] before attempting reseeding.
+    fn new(threshold: u64, mut reseeder: Rsdr) -> Result<Self, Rsdr::Error> {
         // Because generating more values than `i64::MAX` takes centuries on
         // current hardware, we just clamp to that value.
         // Also we set a threshold of 0, which indicates no limit, to that
@@ -190,12 +194,14 @@ where
             i64::MAX
         };
 
-        ReseedingCore {
-            inner: rng,
+        let inner = R::try_from_rng(&mut reseeder)?;
+
+        Ok(ReseedingCore {
+            inner,
             reseeder,
             threshold,
             bytes_until_reseed: threshold,
-        }
+        })
     }
 
     /// Reseed the internal PRNG.
@@ -249,16 +255,15 @@ where
 mod test {
     use crate::rngs::mock::StepRng;
     use crate::rngs::std::Core;
-    use crate::{Rng, SeedableRng};
+    use crate::Rng;
 
     use super::ReseedingRng;
 
     #[test]
     fn test_reseeding() {
-        let mut zero = StepRng::new(0, 0);
-        let rng = Core::from_rng(&mut zero);
+        let zero = StepRng::new(0, 0);
         let thresh = 1; // reseed every time the buffer is exhausted
-        let mut reseeding = ReseedingRng::new(rng, thresh, zero);
+        let mut reseeding = ReseedingRng::<Core, _>::new(thresh, zero).unwrap();
 
         // RNG buffer size is [u32; 64]
         // Debug is only implemented up to length 32 so use two arrays
@@ -276,9 +281,8 @@ mod test {
     #[test]
     #[allow(clippy::redundant_clone)]
     fn test_clone_reseeding() {
-        let mut zero = StepRng::new(0, 0);
-        let rng = Core::from_rng(&mut zero);
-        let mut rng1 = ReseedingRng::new(rng, 32 * 4, zero);
+        let zero = StepRng::new(0, 0);
+        let mut rng1 = ReseedingRng::<Core, _>::new(32 * 4, zero).unwrap();
 
         let first: u32 = rng1.random();
         for _ in 0..10 {
diff --git a/src/rngs/thread.rs b/src/rngs/thread.rs
index 64ca0e1f76..38446759ab 100644
--- a/src/rngs/thread.rs
+++ b/src/rngs/thread.rs
@@ -13,7 +13,7 @@ use std::fmt;
 use std::rc::Rc;
 use std::thread_local;
 
-use rand_core::{CryptoRng, RngCore, SeedableRng};
+use rand_core::{CryptoRng, RngCore};
 
 use super::std::Core;
 use crate::rngs::OsRng;
@@ -119,11 +119,9 @@ thread_local!(
     // We require Rc<..> to avoid premature freeing when ThreadRng is used
     // within thread-local destructors. See #968.
     static THREAD_RNG_KEY: Rc<UnsafeCell<ReseedingRng<Core, OsRng>>> = {
-        let r = Core::try_from_os_rng().unwrap_or_else(|err|
+        let rng = ReseedingRng::new(THREAD_RNG_RESEED_THRESHOLD,
+                                    OsRng).unwrap_or_else(|err|
                 panic!("could not initialize ThreadRng: {}", err));
-        let rng = ReseedingRng::new(r,
-                                    THREAD_RNG_RESEED_THRESHOLD,
-                                    OsRng);
         Rc::new(UnsafeCell::new(rng))
     }
 );