diff --git a/src/header.rs b/src/header.rs
index f9aff4f..5882f85 100644
--- a/src/header.rs
+++ b/src/header.rs
@@ -1,10 +1,8 @@
-use std::alloc::Layout;
-use std::cell::Cell;
-use std::fmt;
-use std::sync::atomic::{AtomicUsize, Ordering};
-use std::task::Waker;
-
-use crossbeam_utils::Backoff;
+use core::alloc::Layout;
+use core::cell::UnsafeCell;
+use core::fmt;
+use core::sync::atomic::{AtomicUsize, Ordering};
+use core::task::Waker;
 
 use crate::raw::TaskVTable;
 use crate::state::*;
@@ -22,7 +20,7 @@
     /// The task that is blocked on the `JoinHandle`.
     ///
     /// This waker needs to be woken up once the task completes or is closed.
-    pub(crate) awaiter: Cell<Option<Waker>>,
+    pub(crate) awaiter: UnsafeCell<Option<Waker>>,
 
     /// The virtual table.
     ///
@@ -55,7 +53,7 @@
                 Ok(_) => {
                     // Notify the awaiter that the task has been closed.
                     if state & AWAITER != 0 {
-                        self.notify();
+                        self.notify(None);
                     }
 
                     break;
@@ -67,68 +65,105 @@
 
     /// Notifies the awaiter blocked on this task.
     ///
-    /// If there is a registered waker, it will be removed from the header and woken up.
+    /// If the awaiter is the same as the current waker, it will not be notified.
     #[inline]
-    pub(crate) fn notify(&self) {
-        if let Some(waker) = self.swap_awaiter(None) {
-            // We need a safeguard against panics because waking can panic.
-            abort_on_panic(|| {
-                waker.wake();
-            });
-        }
-    }
+    pub(crate) fn notify(&self, current: Option<&Waker>) {
+        // Mark the awaiter as being notified.
+        let state = self.state.fetch_or(NOTIFYING, Ordering::AcqRel);
 
-    /// Notifies the awaiter blocked on this task, unless its waker matches `current`.
-    ///
-    /// If there is a registered waker, it will be removed from the header in any case.
-    #[inline]
-    pub(crate) fn notify_unless(&self, current: &Waker) {
-        if let Some(waker) = self.swap_awaiter(None) {
-            if !waker.will_wake(current) {
+        // If the awaiter was not being notified nor registered...
+        if state & (NOTIFYING | REGISTERING) == 0 {
+            // Take the waker out.
+            let waker = unsafe { (*self.awaiter.get()).take() };
+
+            // Mark the state as not being notified anymore nor containing an awaiter.
+            self.state
+                .fetch_and(!NOTIFYING & !AWAITER, Ordering::Release);
+
+            if let Some(w) = waker {
                 // We need a safeguard against panics because waking can panic.
-                abort_on_panic(|| {
-                    waker.wake();
+                abort_on_panic(|| match current {
+                    None => w.wake(),
+                    Some(c) if !w.will_wake(c) => w.wake(),
+                    Some(_) => {}
                 });
             }
         }
     }
 
-    /// Swaps the awaiter for a new waker and returns the previous value.
+    /// Registers a new awaiter blocked on this task.
+    ///
+    /// This method is called when `JoinHandle` is polled and the task has not completed.
     #[inline]
-    pub(crate) fn swap_awaiter(&self, new: Option<Waker>) -> Option<Waker> {
-        let new_is_none = new.is_none();
+    pub(crate) fn register(&self, waker: &Waker) {
+        // Load the state and synchronize with it.
+        let mut state = self.state.fetch_or(0, Ordering::Acquire);
 
-        // We're about to try acquiring the lock in a loop. If it's already being held by another
-        // thread, we'll have to spin for a while so it's best to employ a backoff strategy.
-        let backoff = Backoff::new();
         loop {
-            // Acquire the lock. If we're storing an awaiter, then also set the awaiter flag.
-            let state = if new_is_none {
-                self.state.fetch_or(LOCKED, Ordering::Acquire)
-            } else {
-                self.state.fetch_or(LOCKED | AWAITER, Ordering::Acquire)
-            };
+            // There can't be two concurrent registrations because `JoinHandle` can only be polled
+            // by a unique pinned reference.
+            debug_assert!(state & REGISTERING == 0);
 
-            // If the lock was acquired, break from the loop.
-            if state & LOCKED == 0 {
-                break;
+            // If the state is being notified at this moment, just wake and return without
+            // registering.
+            if state & NOTIFYING != 0 {
+                waker.wake_by_ref();
+                return;
             }
 
-            // Snooze for a little while because the lock is held by another thread.
-            backoff.snooze();
+            // Mark the state to let other threads know we're registering a new awaiter.
+            match self.state.compare_exchange_weak(
+                state,
+                state | REGISTERING,
+                Ordering::AcqRel,
+                Ordering::Acquire,
+            ) {
+                Ok(_) => {
+                    state |= REGISTERING;
+                    break;
+                }
+                Err(s) => state = s,
+            }
         }
 
-        // Replace the awaiter.
-        let old = self.awaiter.replace(new);
-
-        // Release the lock. If we've cleared the awaiter, then also unset the awaiter flag.
-        if new_is_none {
-            self.state.fetch_and(!LOCKED & !AWAITER, Ordering::Release);
-        } else {
-            self.state.fetch_and(!LOCKED, Ordering::Release);
+        // Put the waker into the awaiter field.
+        unsafe {
+            abort_on_panic(|| (*self.awaiter.get()) = Some(waker.clone()));
         }
 
-        old
+        // This variable will contain the newly registered waker if a notification comes in before
+        // we complete registration.
+        let mut waker = None;
+
+        loop {
+            // If there was a notification, take the waker out of the awaiter field.
+            if state & NOTIFYING != 0 {
+                if let Some(w) = unsafe { (*self.awaiter.get()).take() } {
+                    waker = Some(w);
+                }
+            }
+
+            // The new state is not being notified nor registered, but there might or might not be
+            // an awaiter depending on whether there was a concurrent notification.
+            let new = if waker.is_none() {
+                (state & !NOTIFYING & !REGISTERING) | AWAITER
+            } else {
+                state & !NOTIFYING & !REGISTERING & !AWAITER
+            };
+
+            match self
+                .state
+                .compare_exchange_weak(state, new, Ordering::AcqRel, Ordering::Acquire)
+            {
+                Ok(_) => break,
+                Err(s) => state = s,
+            }
+        }
+
+        // If there was a notification during registration, wake the awaiter now.
+        if let Some(w) = waker {
+            abort_on_panic(|| w.wake());
+        }
     }
 
     /// Returns the offset at which the tag of type `T` is stored.
diff --git a/src/join_handle.rs b/src/join_handle.rs
index 9357d32..49d529b 100644
--- a/src/join_handle.rs
+++ b/src/join_handle.rs
@@ -1,10 +1,10 @@
-use std::fmt;
-use std::future::Future;
-use std::marker::{PhantomData, Unpin};
-use std::pin::Pin;
-use std::ptr::NonNull;
-use std::sync::atomic::Ordering;
-use std::task::{Context, Poll};
+use core::fmt;
+use core::future::Future;
+use core::marker::{PhantomData, Unpin};
+use core::pin::Pin;
+use core::ptr::NonNull;
+use core::sync::atomic::Ordering;
+use core::task::{Context, Poll};
 
 use crate::header::Header;
 use crate::state::*;
@@ -71,7 +71,7 @@
 
                         // Notify the awaiter that the task has been closed.
                         if state & AWAITER != 0 {
-                            (*header).notify();
+                            (*header).notify(None);
                         }
 
                         break;
@@ -190,7 +190,7 @@
                 if state & CLOSED != 0 {
                     // Even though the awaiter is most likely the current task, it could also be
                     // another task.
-                    (*header).notify_unless(cx.waker());
+                    (*header).notify(Some(cx.waker()));
                     return Poll::Ready(None);
                 }
 
@@ -199,7 +199,7 @@
                     // Replace the waker with one associated with the current task. We need a
                     // safeguard against panics because dropping the previous waker can panic.
                     abort_on_panic(|| {
-                        (*header).swap_awaiter(Some(cx.waker().clone()));
+                        (*header).register(cx.waker());
                     });
 
                     // Reload the state after registering. It is possible that the task became
@@ -230,7 +230,7 @@
                         // Notify the awaiter. Even though the awaiter is most likely the current
                         // task, it could also be another task.
                         if state & AWAITER != 0 {
-                            (*header).notify_unless(cx.waker());
+                            (*header).notify(Some(cx.waker()));
                         }
 
                         // Take the output from the task.
diff --git a/src/lib.rs b/src/lib.rs
index a265679..5fe858a 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -97,10 +97,13 @@
 //! [`Task`]: struct.Task.html
 //! [`JoinHandle`]: struct.JoinHandle.html
 
+#![no_std]
 #![warn(missing_docs, missing_debug_implementations, rust_2018_idioms)]
 #![doc(test(attr(deny(rust_2018_idioms, warnings))))]
 #![doc(test(attr(allow(unused_extern_crates, unused_variables))))]
 
+extern crate alloc;
+
 mod header;
 mod join_handle;
 mod raw;
diff --git a/src/raw.rs b/src/raw.rs
index c250c02..6af184f 100644
--- a/src/raw.rs
+++ b/src/raw.rs
@@ -1,12 +1,12 @@
-use std::alloc::{self, Layout};
-use std::cell::Cell;
-use std::future::Future;
-use std::marker::PhantomData;
-use std::mem::{self, ManuallyDrop};
-use std::pin::Pin;
-use std::ptr::NonNull;
-use std::sync::atomic::{AtomicUsize, Ordering};
-use std::task::{Context, Poll, RawWaker, RawWakerVTable, Waker};
+use alloc::alloc::Layout;
+use core::cell::UnsafeCell;
+use core::future::Future;
+use core::marker::PhantomData;
+use core::mem::{self, ManuallyDrop};
+use core::pin::Pin;
+use core::ptr::NonNull;
+use core::sync::atomic::{AtomicUsize, Ordering};
+use core::task::{Context, Poll, RawWaker, RawWakerVTable, Waker};
 
 use crate::header::Header;
 use crate::state::*;
@@ -107,8 +107,8 @@
 
         unsafe {
             // Allocate enough space for the entire task.
-            let raw_task = match NonNull::new(alloc::alloc(task_layout.layout) as *mut ()) {
-                None => std::process::abort(),
+            let raw_task = match NonNull::new(alloc::alloc::alloc(task_layout.layout) as *mut ()) {
+                None => libc::abort(),
                 Some(p) => p,
             };
 
@@ -117,7 +117,7 @@
             // Write the header as the first field of the task.
             (raw.header as *mut Header).write(Header {
                 state: AtomicUsize::new(SCHEDULED | HANDLE | REFERENCE),
-                awaiter: Cell::new(None),
+                awaiter: UnsafeCell::new(None),
                 vtable: &TaskVTable {
                     raw_waker_vtable: RawWakerVTable::new(
                         Self::clone_waker,
@@ -307,7 +307,7 @@
                         if state & RUNNING == 0 {
                             // If the reference count overflowed, abort.
                             if state > isize::max_value() as usize {
-                                std::process::abort();
+                                libc::abort();
                             }
 
                             // Schedule the task. There is no need to call `Self::schedule(ptr)`
@@ -339,7 +339,7 @@
 
         // If the reference count overflowed, abort.
         if state > isize::max_value() as usize {
-            std::process::abort();
+            libc::abort();
         }
 
         RawWaker::new(ptr, raw_waker_vtable)
@@ -449,7 +449,7 @@
         });
 
         // Finally, deallocate the memory reserved by the task.
-        alloc::dealloc(ptr as *mut u8, task_layout.layout);
+        alloc::alloc::dealloc(ptr as *mut u8, task_layout.layout);
     }
 
     /// Runs a task.
@@ -474,7 +474,7 @@
             if state & CLOSED != 0 {
                 // Notify the awaiter that the task has been closed.
                 if state & AWAITER != 0 {
-                    (*raw.header).notify();
+                    (*raw.header).notify(None);
                 }
 
                 // Drop the future.
@@ -542,7 +542,7 @@
 
                             // Notify the awaiter that the task has been completed.
                             if state & AWAITER != 0 {
-                                (*raw.header).notify();
+                                (*raw.header).notify(None);
                             }
 
                             // Drop the task reference.
@@ -649,7 +649,7 @@
 
                                 // Notify the awaiter that the task has been closed.
                                 if state & AWAITER != 0 {
-                                    (*raw.header).notify();
+                                    (*raw.header).notify(None);
                                 }
 
                                 // Drop the task reference.
diff --git a/src/state.rs b/src/state.rs
index c03fea3..167a371 100644
--- a/src/state.rs
+++ b/src/state.rs
@@ -48,10 +48,16 @@
 /// check that tells us if we need to wake anyone without acquiring the lock inside the task.
 pub(crate) const AWAITER: usize = 1 << 5;
 
-/// Set if the awaiter is locked.
+/// Set if an awaiter is being registered.
 ///
-/// This lock is acquired before a new awaiter is registered or the existing one is woken up.
-pub(crate) const LOCKED: usize = 1 << 6;
+/// This flag is set when `JoinHandle` is polled and we are registering a new awaiter.
+pub(crate) const REGISTERING: usize = 1 << 6;
+
+/// Set if the awaiter is being notified.
+///
+/// This flag is set when notifying the awaiter. If an awaiter is concurrently registered and
+/// notified, whichever side came first will take over the reposibility of resolving the race.
+pub(crate) const NOTIFYING: usize = 1 << 7;
 
 /// A single reference.
 ///
@@ -61,4 +67,4 @@
 ///
 /// Note that the reference counter only tracks the `Task` and `Waker`s. The `JoinHandle` is
 /// tracked separately by the `HANDLE` flag.
-pub(crate) const REFERENCE: usize = 1 << 7;
+pub(crate) const REFERENCE: usize = 1 << 8;
diff --git a/src/task.rs b/src/task.rs
index 83cdf79..80953f4 100644
--- a/src/task.rs
+++ b/src/task.rs
@@ -1,11 +1,10 @@
-use std::fmt;
-use std::future::Future;
-use std::marker::PhantomData;
-use std::mem::{self, ManuallyDrop};
-use std::pin::Pin;
-use std::ptr::NonNull;
-use std::task::{Context, Poll};
-use std::thread::{self, ThreadId};
+use core::fmt;
+use core::future::Future;
+use core::marker::PhantomData;
+use core::mem::{self, ManuallyDrop};
+use core::pin::Pin;
+use core::ptr::NonNull;
+use core::task::{Context, Poll};
 
 use crate::header::Header;
 use crate::raw::RawTask;
@@ -109,20 +108,29 @@
     S: Fn(Task<T>) + Send + Sync + 'static,
     T: Send + Sync + 'static,
 {
-    thread_local! {
-        static ID: ThreadId = thread::current().id();
+    #[cfg(unix)]
+    #[inline]
+    fn thread_id() -> usize {
+        unsafe { libc::pthread_self() as usize }
+    }
+
+    #[cfg(windows)]
+    #[inline]
+    fn thread_id() -> usize {
+        unsafe { winapi::um::processthreadsapi::GetCurrentThreadId() as usize }
     }
 
     struct Checked<F> {
-        id: ThreadId,
+        id: usize,
         inner: ManuallyDrop<F>,
     }
 
     impl<F> Drop for Checked<F> {
         fn drop(&mut self) {
-            if ID.with(|id| *id) != self.id {
-                panic!("local task dropped by a thread that didn't spawn it");
-            }
+            assert!(
+                self.id == thread_id(),
+                "local task dropped by a thread that didn't spawn it"
+            );
             unsafe {
                 ManuallyDrop::drop(&mut self.inner);
             }
@@ -133,15 +141,16 @@
         type Output = F::Output;
 
         fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
-            if ID.with(|id| *id) != self.id {
-                panic!("local task polled by a thread that didn't spawn it");
-            }
+            assert!(
+                self.id == thread_id(),
+                "local task polled by a thread that didn't spawn it"
+            );
             unsafe { self.map_unchecked_mut(|c| &mut *c.inner).poll(cx) }
         }
     }
 
     let future = Checked {
-        id: ID.with(|id| *id),
+        id: thread_id(),
         inner: ManuallyDrop::new(future),
     };
 
diff --git a/src/utils.rs b/src/utils.rs
index 441ead1..7c71deb 100644
--- a/src/utils.rs
+++ b/src/utils.rs
@@ -1,5 +1,5 @@
-use std::alloc::Layout;
-use std::mem;
+use core::alloc::Layout;
+use core::mem;
 
 /// Calls a function and aborts if it panics.
 ///
@@ -10,7 +10,7 @@
 
     impl Drop for Bomb {
         fn drop(&mut self) {
-            std::process::abort();
+            unsafe { libc::abort() }
         }
     }