diff --git a/crossbeam-epoch/Cargo.toml b/crossbeam-epoch/Cargo.toml
index b9aacdcbb..fe111e720 100644
--- a/crossbeam-epoch/Cargo.toml
+++ b/crossbeam-epoch/Cargo.toml
@@ -19,7 +19,7 @@ default = ["std"]
 
 # Enable to use APIs that require `std`.
 # This is enabled by default.
-std = ["alloc", "crossbeam-utils/std", "lazy_static"]
+std = ["alloc", "crossbeam-utils/std", "once_cell"]
 
 # Enable to use APIs that require `alloc`.
 # This is enabled by default and also enabled if the `std` feature is enabled.
@@ -48,6 +48,8 @@ autocfg = "1"
 [dependencies]
 cfg-if = "1"
 memoffset = "0.6"
+once_cell = { version = "1", optional = true }
+scopeguard = { version = "1.1", default-features = false }
 
 # Enable the use of loom for concurrency testing.
 #
@@ -61,14 +63,6 @@ version = "0.8.5"
 path = "../crossbeam-utils"
 default-features = false
 
-[dependencies.lazy_static]
-version = "1.4.0"
-optional = true
-
-[dependencies.scopeguard]
-version = "1.1.0"
-default-features = false
-
 [dev-dependencies]
 rand = "0.8"
 rustversion = "1"
diff --git a/crossbeam-epoch/src/default.rs b/crossbeam-epoch/src/default.rs
index b7797ce96..180a791c9 100644
--- a/crossbeam-epoch/src/default.rs
+++ b/crossbeam-epoch/src/default.rs
@@ -6,9 +6,17 @@
 
 use crate::collector::{Collector, LocalHandle};
 use crate::guard::Guard;
-use crate::primitive::{lazy_static, thread_local};
+use crate::primitive::thread_local;
+#[cfg(not(crossbeam_loom))]
+use once_cell::sync::Lazy;
 
-lazy_static! {
+/// The global data for the default garbage collector.
+#[cfg(not(crossbeam_loom))]
+static COLLECTOR: Lazy<Collector> = Lazy::new(Collector::new);
+// FIXME: loom does not currently provide the equivalent of Lazy:
+// https://github.com/crossbeam-rs/crossbeam/issues/623
+#[cfg(crossbeam_loom)]
+loom::lazy_static! {
     /// The global data for the default garbage collector.
     static ref COLLECTOR: Collector = Collector::new();
 }
diff --git a/crossbeam-epoch/src/lib.rs b/crossbeam-epoch/src/lib.rs
index 7150ec6f7..4cf982b6b 100644
--- a/crossbeam-epoch/src/lib.rs
+++ b/crossbeam-epoch/src/lib.rs
@@ -88,7 +88,6 @@ mod primitive {
         }
         pub(crate) use loom::sync::Arc;
     }
-    pub(crate) use loom::lazy_static;
     pub(crate) use loom::thread_local;
 }
 #[cfg(not(crossbeam_no_atomic_cas))]
@@ -135,9 +134,6 @@ mod primitive {
 
     #[cfg(feature = "std")]
     pub(crate) use std::thread_local;
-
-    #[cfg(feature = "std")]
-    pub(crate) use lazy_static::lazy_static;
 }
 
 #[cfg(not(crossbeam_no_atomic_cas))]
diff --git a/crossbeam-utils/Cargo.toml b/crossbeam-utils/Cargo.toml
index 0c2eebf1b..5b0849c1a 100644
--- a/crossbeam-utils/Cargo.toml
+++ b/crossbeam-utils/Cargo.toml
@@ -19,7 +19,7 @@ default = ["std"]
 
 # Enable to use APIs that require `std`.
 # This is enabled by default.
-std = ["lazy_static"]
+std = ["once_cell"]
 
 # These features are no longer used.
 # TODO: remove in the next major version.
@@ -32,7 +32,7 @@ nightly = []
 
 [dependencies]
 cfg-if = "1"
-lazy_static = { version = "1.4.0", optional = true }
+once_cell = { version = "1", optional = true }
 
 # Enable the use of loom for concurrency testing.
 #
diff --git a/crossbeam-utils/src/sync/sharded_lock.rs b/crossbeam-utils/src/sync/sharded_lock.rs
index 163d34c81..692653447 100644
--- a/crossbeam-utils/src/sync/sharded_lock.rs
+++ b/crossbeam-utils/src/sync/sharded_lock.rs
@@ -10,7 +10,7 @@ use std::sync::{Mutex, RwLock, RwLockReadGuard, RwLockWriteGuard};
 use std::thread::{self, ThreadId};
 
 use crate::CachePadded;
-use lazy_static::lazy_static;
+use once_cell::sync::Lazy;
 
 /// The number of shards per sharded lock. Must be a power of two.
 const NUM_SHARDS: usize = 8;
@@ -583,13 +583,13 @@ struct ThreadIndices {
     next_index: usize,
 }
 
-lazy_static! {
-    static ref THREAD_INDICES: Mutex<ThreadIndices> = Mutex::new(ThreadIndices {
+static THREAD_INDICES: Lazy<Mutex<ThreadIndices>> = Lazy::new(|| {
+    Mutex::new(ThreadIndices {
         mapping: HashMap::new(),
         free_list: Vec::new(),
         next_index: 0,
-    });
-}
+    })
+});
 
 /// A registration of a thread with an index.
 ///