diff --git a/futures-util/src/compat/compat01as03.rs b/futures-util/src/compat/compat01as03.rs
index d63d73c7dc..a48518264f 100644
--- a/futures-util/src/compat/compat01as03.rs
+++ b/futures-util/src/compat/compat01as03.rs
@@ -9,6 +9,7 @@ use futures_core::{future::Future as Future03, stream::Stream as Stream03, task
 #[cfg(feature = "sink")]
 use futures_sink::Sink as Sink03;
 use std::boxed::Box;
+use std::cell::UnsafeCell;
 use std::pin::Pin;
 use std::task::Context;
 
@@ -319,33 +320,45 @@ where
     }
 }
 
-struct NotifyWaker(task03::Waker);
+#[repr(transparent)]
+struct NotifyWaker(UnsafeCell<task03::Waker>);
 
 #[derive(Clone)]
 struct WakerToHandle<'a>(&'a task03::Waker);
 
 impl From<WakerToHandle<'_>> for NotifyHandle01 {
     fn from(handle: WakerToHandle<'_>) -> Self {
-        let ptr = Box::new(NotifyWaker(handle.0.clone()));
+        let waker_ptr: Box<task03::Waker> = Box::new(handle.0.clone());
+        // NotifyWaker is a transparent (pointer compatible) wrapper for
+        // task03::Waker (and wrapping in UnsafeCell is fine).
+        let ptr: *mut NotifyWaker = Box::into_raw(waker_ptr) as *mut NotifyWaker;
 
-        unsafe { Self::new(Box::into_raw(ptr)) }
+        unsafe { Self::new(ptr) }
     }
 }
 
 impl Notify01 for NotifyWaker {
     fn notify(&self, _: usize) {
-        self.0.wake_by_ref();
+        unsafe { &*self.0.get() }.wake_by_ref();
     }
 }
 
+unsafe impl Send for NotifyWaker {}
+unsafe impl Sync for NotifyWaker {}
+
 unsafe impl UnsafeNotify01 for NotifyWaker {
     unsafe fn clone_raw(&self) -> NotifyHandle01 {
-        WakerToHandle(&self.0).into()
+        WakerToHandle(unsafe { &*self.0.get() }).into()
     }
 
     unsafe fn drop_raw(&self) {
-        let ptr: *const dyn UnsafeNotify01 = self;
-        drop(unsafe { Box::from_raw(ptr as *mut dyn UnsafeNotify01) });
+        /* UnsafeNotify01::drop_raw says this should receive `*mut Self`,
+         * but that isn't dyn compatible.
+         * miri is unhappy when a `*mut` is created from a `&` reference,
+         * so need to go through `UnsafeCell`.
+         */
+        let waker: *mut task03::Waker = self.0.get();
+        drop(unsafe { Box::from_raw(waker) });
     }
 }
 
diff --git a/futures/tests/compat_miri.rs b/futures/tests/compat_miri.rs
new file mode 100644
index 0000000000..b5ccaa4612
--- /dev/null
+++ b/futures/tests/compat_miri.rs
@@ -0,0 +1,14 @@
+#![cfg(feature = "compat")]
+use futures::compat::Future01CompatExt;
+use futures::executor::block_on;
+use futures::future::TryFutureExt;
+
+#[test]
+// from https://github.com/rust-lang/futures-rs/issues/2514
+fn miri_compat_two_way() {
+    let fut = async { Ok(()) as Result<(), ()> };
+    let fut = Box::pin(fut);
+    let fut = fut.compat(); // 03as01
+    let fut = fut.compat(); // 01as03
+    block_on(fut).unwrap();
+}