diff --git a/roaring/src/bitmap/iter.rs b/roaring/src/bitmap/iter.rs
index 1593ab40..4076950d 100644
--- a/roaring/src/bitmap/iter.rs
+++ b/roaring/src/bitmap/iter.rs
@@ -96,6 +96,43 @@ impl Iterator for Iter<'_> {
         };
         init
     }
+
+    fn count(self) -> usize
+    where
+        Self: Sized,
+    {
+        let mut count = self.front.map_or(0, Iterator::count);
+        count += self.containers.map(|container| container.len() as usize).sum::<usize>();
+        count += self.back.map_or(0, Iterator::count);
+        count
+    }
+
+    fn nth(&mut self, n: usize) -> Option<Self::Item> {
+        let mut n = n;
+        let nth_advance = |it: &mut container::Iter| {
+            let len = it.len();
+            if n < len {
+                it.nth(n)
+            } else {
+                n -= len;
+                None
+            }
+        };
+        if let Some(x) = and_then_or_clear(&mut self.front, nth_advance) {
+            return Some(x);
+        }
+        for container in self.containers.by_ref() {
+            let len = container.len() as usize;
+            if n < len {
+                let mut front_iter = container.into_iter();
+                let result = front_iter.nth(n);
+                self.front = Some(front_iter);
+                return result;
+            }
+            n -= len;
+        }
+        self.back.as_mut().and_then(|it| it.nth(n))
+    }
 }
 
 impl DoubleEndedIterator for Iter<'_> {
@@ -128,6 +165,33 @@ impl DoubleEndedIterator for Iter<'_> {
         };
         init
     }
+
+    fn nth_back(&mut self, n: usize) -> Option<Self::Item> {
+        let mut n = n;
+        let nth_advance = |it: &mut container::Iter| {
+            let len = it.len();
+            if n < len {
+                it.nth_back(n)
+            } else {
+                n -= len;
+                None
+            }
+        };
+        if let Some(x) = and_then_or_clear(&mut self.back, nth_advance) {
+            return Some(x);
+        }
+        for container in self.containers.by_ref().rev() {
+            let len = container.len() as usize;
+            if n < len {
+                let mut front_iter = container.into_iter();
+                let result = front_iter.nth_back(n);
+                self.back = Some(front_iter);
+                return result;
+            }
+            n -= len;
+        }
+        self.front.as_mut().and_then(|it| it.nth_back(n))
+    }
 }
 
 #[cfg(target_pointer_width = "64")]
@@ -170,6 +234,43 @@ impl Iterator for IntoIter {
         };
         init
     }
+
+    fn count(self) -> usize
+    where
+        Self: Sized,
+    {
+        let mut count = self.front.map_or(0, Iterator::count);
+        count += self.containers.map(|container| container.len() as usize).sum::<usize>();
+        count += self.back.map_or(0, Iterator::count);
+        count
+    }
+
+    fn nth(&mut self, n: usize) -> Option<Self::Item> {
+        let mut n = n;
+        let nth_advance = |it: &mut container::Iter| {
+            let len = it.len();
+            if n < len {
+                it.nth(n)
+            } else {
+                n -= len;
+                None
+            }
+        };
+        if let Some(x) = and_then_or_clear(&mut self.front, nth_advance) {
+            return Some(x);
+        }
+        for container in self.containers.by_ref() {
+            let len = container.len() as usize;
+            if n < len {
+                let mut front_iter = container.into_iter();
+                let result = front_iter.nth(n);
+                self.front = Some(front_iter);
+                return result;
+            }
+            n -= len;
+        }
+        self.back.as_mut().and_then(|it| it.nth(n))
+    }
 }
 
 impl DoubleEndedIterator for IntoIter {
@@ -202,6 +303,33 @@ impl DoubleEndedIterator for IntoIter {
         };
         init
     }
+
+    fn nth_back(&mut self, n: usize) -> Option<Self::Item> {
+        let mut n = n;
+        let nth_advance = |it: &mut container::Iter| {
+            let len = it.len();
+            if n < len {
+                it.nth_back(n)
+            } else {
+                n -= len;
+                None
+            }
+        };
+        if let Some(x) = and_then_or_clear(&mut self.back, nth_advance) {
+            return Some(x);
+        }
+        for container in self.containers.by_ref().rev() {
+            let len = container.len() as usize;
+            if n < len {
+                let mut front_iter = container.into_iter();
+                let result = front_iter.nth_back(n);
+                self.back = Some(front_iter);
+                return result;
+            }
+            n -= len;
+        }
+        self.front.as_mut().and_then(|it| it.nth_back(n))
+    }
 }
 
 #[cfg(target_pointer_width = "64")]
diff --git a/roaring/tests/iter.rs b/roaring/tests/iter.rs
index 86a83245..05591681 100644
--- a/roaring/tests/iter.rs
+++ b/roaring/tests/iter.rs
@@ -81,6 +81,53 @@ proptest! {
     }
 }
 
+proptest! {
+    #[test]
+    fn nth(values in btree_set(any::<u32>(), ..=10_000), nth in 0..10_005usize) {
+        let bitmap = RoaringBitmap::from_sorted_iter(values.iter().cloned()).unwrap();
+        let mut orig_iter = bitmap.iter().fuse();
+        let mut iter = bitmap.iter();
+
+        for _ in 0..nth {
+            if orig_iter.next().is_none() {
+                break;
+            }
+        }
+        let expected = orig_iter.next();
+        assert_eq!(expected, iter.nth(nth));
+        let expected_next = orig_iter.next();
+        assert_eq!(expected_next, iter.next());
+
+        let mut val_iter = values.into_iter();
+        assert_eq!(expected, val_iter.nth(nth));
+        assert_eq!(expected_next, val_iter.next());
+    }
+}
+
+#[test]
+fn huge_nth() {
+    let bitmap = RoaringBitmap::new();
+    let mut iter = bitmap.iter();
+    assert_eq!(None, iter.nth(usize::MAX));
+}
+
+proptest! {
+    #[test]
+    fn count(values in btree_set(any::<u32>(), ..=10_000), skip in 0..10_005usize) {
+        let bitmap = RoaringBitmap::from_sorted_iter(values.iter().cloned()).unwrap();
+        let mut iter = bitmap.iter();
+
+        if let Some(n) = skip.checked_sub(1) {
+            iter.nth(n);
+        }
+        let expected_count = values.len().saturating_sub(skip);
+        let size_hint = iter.size_hint();
+        assert_eq!(expected_count, size_hint.0);
+        assert_eq!(Some(expected_count), size_hint.1);
+        assert_eq!(expected_count, iter.count());
+    }
+}
+
 #[test]
 fn rev_array() {
     let values = 0..100;