diff --git a/src/covariant_cell_option.rs b/src/covariant_cell_option.rs
new file mode 100644
index 0000000..ac8b12b
--- /dev/null
+++ b/src/covariant_cell_option.rs
@@ -0,0 +1,59 @@
+//! A `Cell<Option<F>>`, but covariant, at the cost of a very reduced API.
+//!
+//! (the idea being: it starts as `Some(F)`, and the only `&`-based operation
+//! is `take()`ing it. This guarantees covariance to be fine, since the `F`
+//! value is never overwritten).
+
+use ::core::{cell::Cell, mem::ManuallyDrop};
+
+pub struct CovariantCellOption<F> {
+    /// Invariant: if this is `true` then `value` must contain a non-dropped `F`;
+    is_some: Cell<bool>,
+    value: ManuallyDrop<F>,
+}
+
+impl<F> CovariantCellOption<F> {
+    pub const fn some(value: F) -> Self {
+        Self { is_some: Cell::new(true), value: ManuallyDrop::new(value) }
+    }
+
+    pub fn into_inner(self) -> Option<F> {
+        // Small optimization: disable drop glue so as not to have to overwrite `is_some`.
+        let mut this = ManuallyDrop::new(self);
+        let is_some = this.is_some.get_mut();
+        is_some.then(|| unsafe {
+            // SAFETY: as per the invariant, we can use `value`. We can also *consume* it by doing:
+            // *is_some = false;
+            // but we actually don't even need to do it since we don't use `this` anymore.
+            ManuallyDrop::take(&mut this.value)
+        })
+    }
+
+    pub fn take(&self) -> Option<F> {
+        self.is_some.get().then(|| unsafe {
+            // SAFETY: as per the invariant, we can use `value`.
+            // Clearing the `is_some` flag also lets us *consume* it.
+            self.is_some.set(false);
+            // `ManuallyDrop::take_by_ref`, morally.
+            <*const F>::read(&*self.value)
+        })
+    }
+}
+
+impl<F> Drop for CovariantCellOption<F> {
+    fn drop(&mut self) {
+        if *self.is_some.get_mut() {
+            unsafe {
+                // SAFETY: as per the invariant, we can use `value`.
+                ManuallyDrop::drop(&mut self.value)
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+fn _assert_covariance<'short>(
+    long: *const (CovariantCellOption<&'static ()>,),
+) -> *const (CovariantCellOption<&'short ()>,) {
+    long
+}
diff --git a/src/lib.rs b/src/lib.rs
index 9239296..fc302c2 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -369,6 +369,8 @@
 #[cfg(feature = "alloc")]
 extern crate alloc;
 
+mod covariant_cell_option;
+
 #[cfg(all(feature = "critical-section", not(feature = "std")))]
 #[path = "imp_cs.rs"]
 mod imp;
@@ -384,13 +386,14 @@ mod imp;
 /// Single-threaded version of `OnceCell`.
 pub mod unsync {
     use core::{
-        cell::{Cell, UnsafeCell},
+        cell::UnsafeCell,
         fmt, mem,
         ops::{Deref, DerefMut},
         panic::{RefUnwindSafe, UnwindSafe},
     };
 
     use super::unwrap_unchecked;
+    use crate::covariant_cell_option::CovariantCellOption;
 
     /// A cell which can be written to only once. It is not thread safe.
     ///
@@ -717,7 +720,7 @@ pub mod unsync {
     /// ```
     pub struct Lazy<T, F = fn() -> T> {
         cell: OnceCell<T>,
-        init: Cell<Option<F>>,
+        init: CovariantCellOption<F>,
     }
 
     impl<T, F: RefUnwindSafe> RefUnwindSafe for Lazy<T, F> where OnceCell<T>: RefUnwindSafe {}
@@ -744,7 +747,7 @@ pub mod unsync {
         /// # }
         /// ```
         pub const fn new(init: F) -> Lazy<T, F> {
-            Lazy { cell: OnceCell::new(), init: Cell::new(Some(init)) }
+            Lazy { cell: OnceCell::new(), init: CovariantCellOption::some(init) }
         }
 
         /// Consumes this `Lazy` returning the stored value.
@@ -754,7 +757,8 @@ pub mod unsync {
             let cell = this.cell;
             let init = this.init;
             cell.into_inner().ok_or_else(|| {
-                init.take().unwrap_or_else(|| panic!("Lazy instance has previously been poisoned"))
+                init.into_inner()
+                    .unwrap_or_else(|| panic!("Lazy instance has previously been poisoned"))
             })
         }
     }
@@ -861,13 +865,13 @@ pub mod unsync {
 #[cfg(any(feature = "std", feature = "critical-section"))]
 pub mod sync {
     use core::{
-        cell::Cell,
         fmt, mem,
         ops::{Deref, DerefMut},
         panic::RefUnwindSafe,
     };
 
     use super::{imp::OnceCell as Imp, unwrap_unchecked};
+    use crate::covariant_cell_option::CovariantCellOption;
 
     /// A thread-safe cell which can be written to only once.
     ///
@@ -1253,7 +1257,7 @@ pub mod sync {
     /// ```
     pub struct Lazy<T, F = fn() -> T> {
         cell: OnceCell<T>,
-        init: Cell<Option<F>>,
+        init: CovariantCellOption<F>,
     }
 
     impl<T: fmt::Debug, F> fmt::Debug for Lazy<T, F> {
@@ -1275,7 +1279,7 @@ pub mod sync {
         /// Creates a new lazy value with the given initializing
         /// function.
         pub const fn new(f: F) -> Lazy<T, F> {
-            Lazy { cell: OnceCell::new(), init: Cell::new(Some(f)) }
+            Lazy { cell: OnceCell::new(), init: CovariantCellOption::some(f) }
         }
 
         /// Consumes this `Lazy` returning the stored value.
@@ -1285,7 +1289,8 @@ pub mod sync {
             let cell = this.cell;
             let init = this.init;
             cell.into_inner().ok_or_else(|| {
-                init.take().unwrap_or_else(|| panic!("Lazy instance has previously been poisoned"))
+                init.into_inner()
+                    .unwrap_or_else(|| panic!("Lazy instance has previously been poisoned"))
             })
         }
     }
diff --git a/tests/it.rs b/tests/it.rs
index d18f0a1..5673245 100644
--- a/tests/it.rs
+++ b/tests/it.rs
@@ -1,3 +1,18 @@
+/// Put here any code relying on duck-typed `Lazy` and `OnceCell`, oblivious to
+/// their exact `sync` or `unsync` nature.
+macro_rules! tests_for_both {() => (
+    /// <https://github.com/matklad/once_cell/issues/167>
+    #[test]
+    fn assert_lazy_is_covariant_in_the_ctor() {
+        #[allow(dead_code)]
+        type AnyLazy<'f, T> = Lazy<T, Box<dyn 'f + FnOnce() -> T>>;
+
+        fn _for<'short, T>(it: *const (AnyLazy<'static, T>, )) -> *const (AnyLazy<'short, T>, ) {
+            it
+        }
+    }
+)}
+
 mod unsync {
     use core::{
         cell::Cell,
@@ -6,6 +21,8 @@ mod unsync {
 
     use once_cell::unsync::{Lazy, OnceCell};
 
+    tests_for_both!();
+
     #[test]
     fn once_cell() {
         let c = OnceCell::new();
@@ -263,6 +280,8 @@ mod sync {
 
     use once_cell::sync::{Lazy, OnceCell};
 
+    tests_for_both!();
+
     #[test]
     fn once_cell() {
         let c = OnceCell::new();