diff --git a/crates/test-programs/wasi-tests/src/bin/poll_oneoff.rs b/crates/test-programs/wasi-tests/src/bin/poll_oneoff.rs
index a680cf630900..6407a32f3cb0 100644
--- a/crates/test-programs/wasi-tests/src/bin/poll_oneoff.rs
+++ b/crates/test-programs/wasi-tests/src/bin/poll_oneoff.rs
@@ -26,9 +26,10 @@ unsafe fn test_empty_poll() {
 }
 
 unsafe fn test_timeout() {
+    let timeout = 5_000_000u64; // 5 milliseconds
     let clock = wasi::SubscriptionClock {
         id: wasi::CLOCKID_MONOTONIC,
-        timeout: 5_000_000u64, // 5 milliseconds
+        timeout,
         precision: 0,
         flags: 0,
     };
@@ -39,7 +40,9 @@ unsafe fn test_timeout() {
             u: wasi::SubscriptionUU { clock },
         },
     }];
+    let before = wasi::clock_time_get(wasi::CLOCKID_MONOTONIC, 0).unwrap();
     let out = poll_oneoff_impl(&r#in).unwrap();
+    let after = wasi::clock_time_get(wasi::CLOCKID_MONOTONIC, 0).unwrap();
     assert_eq!(out.len(), 1, "should return 1 event");
     let event = &out[0];
     assert_errno!(event.error, wasi::ERRNO_SUCCESS);
@@ -52,6 +55,42 @@ unsafe fn test_timeout() {
         event.userdata, CLOCK_ID,
         "the event.userdata should contain clock_id specified by the user"
     );
+    assert!(after - before >= timeout, "poll_oneoff should sleep for the specified interval");
+}
+
+// Like test_timeout, but uses `CLOCKID_REALTIME`, as WASI libc's sleep
+// functions do.
+unsafe fn test_sleep() {
+    let timeout = 5_000_000u64; // 5 milliseconds
+    let clock = wasi::SubscriptionClock {
+        id: wasi::CLOCKID_REALTIME,
+        timeout,
+        precision: 0,
+        flags: 0,
+    };
+    let r#in = [wasi::Subscription {
+        userdata: CLOCK_ID,
+        u: wasi::SubscriptionU {
+            tag: wasi::EVENTTYPE_CLOCK,
+            u: wasi::SubscriptionUU { clock },
+        },
+    }];
+    let before = wasi::clock_time_get(wasi::CLOCKID_MONOTONIC, 0).unwrap();
+    let out = poll_oneoff_impl(&r#in).unwrap();
+    let after = wasi::clock_time_get(wasi::CLOCKID_MONOTONIC, 0).unwrap();
+    assert_eq!(out.len(), 1, "should return 1 event");
+    let event = &out[0];
+    assert_errno!(event.error, wasi::ERRNO_SUCCESS);
+    assert_eq!(
+        event.r#type,
+        wasi::EVENTTYPE_CLOCK,
+        "the event.type should equal clock"
+    );
+    assert_eq!(
+        event.userdata, CLOCK_ID,
+        "the event.userdata should contain clock_id specified by the user"
+    );
+    assert!(after - before >= timeout, "poll_oneoff should sleep for the specified interval");
 }
 
 unsafe fn test_fd_readwrite(fd: wasi::Fd, error_code: wasi::Errno) {
@@ -156,6 +195,7 @@ unsafe fn test_fd_readwrite_invalid_fd() {
 
 unsafe fn test_poll_oneoff(dir_fd: wasi::Fd) {
     test_timeout();
+    test_sleep();
     test_empty_poll();
     test_fd_readwrite_valid_fd(dir_fd);
     test_fd_readwrite_invalid_fd();
diff --git a/crates/wasi-common/cap-std-sync/src/sched/unix.rs b/crates/wasi-common/cap-std-sync/src/sched/unix.rs
index 15bbb2913882..ab8be60a0a41 100644
--- a/crates/wasi-common/cap-std-sync/src/sched/unix.rs
+++ b/crates/wasi-common/cap-std-sync/src/sched/unix.rs
@@ -108,6 +108,9 @@ impl WasiSched for SyncSched {
         std::thread::yield_now();
         Ok(())
     }
+    fn sleep(&self, duration: Duration) {
+        std::thread::sleep(duration)
+    }
 }
 
 fn wasi_file_raw_fd(f: &dyn WasiFile) -> Option<RawFd> {
diff --git a/crates/wasi-common/cap-std-sync/src/sched/windows.rs b/crates/wasi-common/cap-std-sync/src/sched/windows.rs
index 03eb41514ceb..93545c404019 100644
--- a/crates/wasi-common/cap-std-sync/src/sched/windows.rs
+++ b/crates/wasi-common/cap-std-sync/src/sched/windows.rs
@@ -128,6 +128,9 @@ impl WasiSched for SyncSched {
         thread::yield_now();
         Ok(())
     }
+    fn sleep(&self, duration: Duration) {
+        std::thread::sleep(duration)
+    }
 }
 
 fn wasi_file_raw_handle(f: &dyn WasiFile) -> Option<RawHandle> {
diff --git a/crates/wasi-common/src/sched.rs b/crates/wasi-common/src/sched.rs
index db2a81f9dbc1..381bb61449a2 100644
--- a/crates/wasi-common/src/sched.rs
+++ b/crates/wasi-common/src/sched.rs
@@ -10,6 +10,7 @@ use subscription::{MonotonicClockSubscription, RwSubscription, Subscription, Sub
 pub trait WasiSched {
     fn poll_oneoff(&self, poll: &Poll) -> Result<(), Error>;
     fn sched_yield(&self) -> Result<(), Error>;
+    fn sleep(&self, duration: Duration);
 }
 
 pub struct Userdata(u64);
diff --git a/crates/wasi-common/src/snapshots/preview_0.rs b/crates/wasi-common/src/snapshots/preview_0.rs
index 65f4823a3e60..d027997122f7 100644
--- a/crates/wasi-common/src/snapshots/preview_0.rs
+++ b/crates/wasi-common/src/snapshots/preview_0.rs
@@ -738,6 +738,30 @@ impl<'a> wasi_unstable::WasiUnstable for WasiCtx {
             return Err(Error::invalid_argument().context("nsubscriptions must be nonzero"));
         }
 
+        // Special-case a `poll_oneoff` which is just sleeping on a single
+        // relative timer event, such as what WASI libc uses to implement sleep
+        // functions. This supports all clock IDs, because POSIX says that
+        // `clock_settime` doesn't effect relative sleeps.
+        if nsubscriptions == 1 {
+            let sub = subs.read()?;
+            if let types::SubscriptionU::Clock(clocksub) = sub.u {
+                if !clocksub
+                    .flags
+                    .contains(types::Subclockflags::SUBSCRIPTION_CLOCK_ABSTIME)
+                {
+                    self.sched.sleep(Duration::from_nanos(clocksub.timeout));
+
+                    events.write(types::Event {
+                        userdata: sub.userdata,
+                        error: types::Errno::Success,
+                        type_: types::Eventtype::Clock,
+                        fd_readwrite: fd_readwrite_empty(),
+                    })?;
+                    return Ok(1);
+                }
+            }
+        }
+
         let table = self.table();
         let mut poll = Poll::new();
 
diff --git a/crates/wasi-common/src/snapshots/preview_1.rs b/crates/wasi-common/src/snapshots/preview_1.rs
index d5ec0a586a7f..ca91b84cc7b1 100644
--- a/crates/wasi-common/src/snapshots/preview_1.rs
+++ b/crates/wasi-common/src/snapshots/preview_1.rs
@@ -909,6 +909,30 @@ impl<'a> wasi_snapshot_preview1::WasiSnapshotPreview1 for WasiCtx {
             return Err(Error::invalid_argument().context("nsubscriptions must be nonzero"));
         }
 
+        // Special-case a `poll_oneoff` which is just sleeping on a single
+        // relative timer event, such as what WASI libc uses to implement sleep
+        // functions. This supports all clock IDs, because POSIX says that
+        // `clock_settime` doesn't effect relative sleeps.
+        if nsubscriptions == 1 {
+            let sub = subs.read()?;
+            if let types::SubscriptionU::Clock(clocksub) = sub.u {
+                if !clocksub
+                    .flags
+                    .contains(types::Subclockflags::SUBSCRIPTION_CLOCK_ABSTIME)
+                {
+                    self.sched.sleep(Duration::from_nanos(clocksub.timeout));
+
+                    events.write(types::Event {
+                        userdata: sub.userdata,
+                        error: types::Errno::Success,
+                        type_: types::Eventtype::Clock,
+                        fd_readwrite: fd_readwrite_empty(),
+                    })?;
+                    return Ok(1);
+                }
+            }
+        }
+
         let table = self.table();
         let mut poll = Poll::new();