diff --git a/.travis.yml b/.travis.yml
index 450a15959..9a563ab47 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -15,12 +15,6 @@ matrix:
     - rust: 1.13.0
       os: linux
       #if: everything!
-      before_script:
-        # rand 0.4.2 requires rust 1.15, and rand-0.3.22 requires rand-0.4  :/
-        # manually lowering the dependency in rayon-core:
-        - sed -i -e 's/^rand = .*$/rand = "=0.3.20"/' rayon-core/Cargo.toml
-        - cargo generate-lockfile
-        - git checkout rayon-core/Cargo.toml
 
     - rust: stable
       os: linux
diff --git a/Cargo.toml b/Cargo.toml
index 873bf62ed..7693c613a 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -27,7 +27,7 @@ default-features = false
 [dev-dependencies]
 docopt = "0.8"
 lazy_static = "1"
-rand = ">= 0.3, < 0.5"
+rand = "0.4"
 serde = "1"
 serde_derive = "1"
 
diff --git a/rayon-core/Cargo.toml b/rayon-core/Cargo.toml
index b918286e6..c98bf6d6f 100644
--- a/rayon-core/Cargo.toml
+++ b/rayon-core/Cargo.toml
@@ -14,7 +14,6 @@ keywords = ["parallel", "thread", "concurrency", "join", "performance"]
 categories = ["concurrency"]
 
 [dependencies]
-rand = ">= 0.3, < 0.5"
 num_cpus = "1.2"
 libc = "0.2.16"
 lazy_static = "1"
@@ -25,3 +24,4 @@ lazy_static = "1"
 version = "0.2.0"
 
 [dev-dependencies]
+rand = "0.4"
diff --git a/rayon-core/src/lib.rs b/rayon-core/src/lib.rs
index 1e85e69f0..c8cbe3ba1 100644
--- a/rayon-core/src/lib.rs
+++ b/rayon-core/src/lib.rs
@@ -37,6 +37,8 @@ extern crate crossbeam_deque;
 extern crate lazy_static;
 extern crate libc;
 extern crate num_cpus;
+
+#[cfg(test)]
 extern crate rand;
 
 #[macro_use]
diff --git a/rayon-core/src/registry.rs b/rayon-core/src/registry.rs
index 18748b344..0fb8e2038 100644
--- a/rayon-core/src/registry.rs
+++ b/rayon-core/src/registry.rs
@@ -7,14 +7,15 @@ use job::Job;
 use internal::task::Task;
 use latch::{LatchProbe, Latch, CountLatch, LockLatch, SpinLatch, TickleLatch};
 use log::Event::*;
-use rand::{self, Rng};
 use sleep::Sleep;
 use std::any::Any;
-use std::cell::{Cell, UnsafeCell};
+use std::cell::Cell;
+use std::collections::hash_map::DefaultHasher;
+use std::hash::Hasher;
 use std::sync::{Arc, Mutex, Once, ONCE_INIT};
+use std::sync::atomic::{AtomicUsize, ATOMIC_USIZE_INIT, Ordering};
 use std::thread;
 use std::mem;
-use std::u32;
 use std::usize;
 use unwind;
 use util::leak;
@@ -460,7 +461,7 @@ pub struct WorkerThread {
     breadth_first: bool,
 
     /// A weak random number generator.
-    rng: UnsafeCell<rand::XorShiftRng>,
+    rng: XorShift64Star,
 
     registry: Arc<Registry>,
 }
@@ -602,17 +603,8 @@ impl WorkerThread {
         if num_threads <= 1 {
             return None;
         }
-        assert!(num_threads < (u32::MAX as usize),
-                "we do not support more than u32::MAX worker threads");
-
-        let start = {
-            // OK to use this UnsafeCell because (a) this data is
-            // confined to current thread, as WorkerThread is not Send
-            // nor Sync and (b) rand crate will not call back into
-            // this method.
-            let rng = &mut *self.rng.get();
-            rng.next_u32() % num_threads as u32
-        } as usize;
+
+        let start = self.rng.next_usize(num_threads);
         (start .. num_threads)
             .chain(0 .. start)
             .filter(|&i| i != self.index)
@@ -646,7 +638,7 @@ unsafe fn main_loop(worker: Deque<JobRef>,
         worker: worker,
         breadth_first: breadth_first,
         index: index,
-        rng: UnsafeCell::new(rand::weak_rng()),
+        rng: XorShift64Star::new(),
         registry: registry.clone(),
     };
     WorkerThread::set_current(&worker_thread);
@@ -716,3 +708,43 @@ pub fn in_worker<OP, R>(op: OP) -> R
         }
     }
 }
+
+/// [xorshift*] is a fast pseudorandom number generator which will
+/// even tolerate weak seeding, as long as it's not zero.
+///
+/// [xorshift*]: https://en.wikipedia.org/wiki/Xorshift#xorshift*
+struct XorShift64Star {
+    state: Cell<u64>,
+}
+
+impl XorShift64Star {
+    fn new() -> Self {
+        // Any non-zero seed will do -- this uses the hash of a global counter.
+        let mut seed = 0;
+        while seed == 0 {
+            let mut hasher = DefaultHasher::new();
+            static COUNTER: AtomicUsize = ATOMIC_USIZE_INIT;
+            hasher.write_usize(COUNTER.fetch_add(1, Ordering::Relaxed));
+            seed = hasher.finish();
+        }
+
+        XorShift64Star {
+            state: Cell::new(seed),
+        }
+    }
+
+    fn next(&self) -> u64 {
+        let mut x = self.state.get();
+        debug_assert_ne!(x, 0);
+        x ^= x >> 12;
+        x ^= x << 25;
+        x ^= x >> 27;
+        self.state.set(x);
+        x.wrapping_mul(0x2545_f491_4f6c_dd1d)
+    }
+
+    /// Return a value from `0..n`.
+    fn next_usize(&self, n: usize) -> usize {
+        (self.next() % n as u64) as usize
+    }
+}
diff --git a/rayon-demo/Cargo.toml b/rayon-demo/Cargo.toml
index e2b473c99..19c59a522 100644
--- a/rayon-demo/Cargo.toml
+++ b/rayon-demo/Cargo.toml
@@ -12,7 +12,7 @@ fixedbitset = "0.1.5"
 glium = "0.20"
 lazy_static = "1"
 odds = "0.3"
-rand = ">= 0.3, < 0.5"
+rand = "0.4"
 regex = "0.2"
 serde = "1"
 serde_derive = "1"