diff --git a/README.md b/README.md
index 494f4b8..7e602aa 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,9 @@
 # pyority_queue
 
 Implementations of priority queues in Python using Rust bindings for speed.
+
+## Purpose
+
+I'm doing this to learn Rust, so don't judge me too hard lol.
+I've noted a few places where I'm unhappy with the implementation (mostly w.r.t. code duplication), but hopefully as I become more comfortable in Rust I can go back and fix those.
+Better to have a bad implementation now than a good implementation never is my view.
diff --git a/src/backing/containers/mod.rs b/src/backing/containers/mod.rs
index 74cfd32..992fa05 100644
--- a/src/backing/containers/mod.rs
+++ b/src/backing/containers/mod.rs
@@ -1,5 +1,7 @@
 mod pair;
 mod py_item;
+mod sift_result;
 
 pub use pair::Pair;
 pub use py_item::PyItem;
+pub use sift_result::{SiftError, SiftResult};
diff --git a/src/backing/containers/pair.rs b/src/backing/containers/pair.rs
index d194835..190cd7b 100644
--- a/src/backing/containers/pair.rs
+++ b/src/backing/containers/pair.rs
@@ -13,11 +13,25 @@ impl<D: Clone, P: PartialOrd + Clone> Pair<D, P> {
         Self { data, priority }
     }
 
-    /// Retrieves the internal data.
-    /// It would be nicer to implement this using [`From`] or [`Into`], but I don't see a way to do that using generics.
+    /// Returns the internal data.
+    /// It might(?) be nicer to implement this using [`From`] or [`Into`], but I don't see a way to do that using generics.
     pub fn data(self) -> D {
         self.data
     }
+
+    pub fn get_data(&self) -> &D {
+        &self.data
+    }
+
+    /// Retrieve the priority associated with the data
+    pub fn get_priority(&self) -> &P {
+        &self.priority
+    }
+
+    /// Update the priority associated with the data
+    pub fn set_priority(&mut self, priority: P) {
+        self.priority = priority
+    }
 }
 
 impl<D: Clone, P: PartialOrd + Clone> PartialOrd for Pair<D, P> {
diff --git a/src/backing/containers/py_item.rs b/src/backing/containers/py_item.rs
index 363c853..f67c853 100644
--- a/src/backing/containers/py_item.rs
+++ b/src/backing/containers/py_item.rs
@@ -48,6 +48,8 @@ impl PartialEq for PyItem {
     }
 }
 
+impl Eq for PyItem {}
+
 impl Hash for PyItem {
     fn hash<H: Hasher>(&self, state: &mut H) {
         // TODO: Should warn or fail instead of defaulting to 0
diff --git a/src/backing/containers/sift_result.rs b/src/backing/containers/sift_result.rs
new file mode 100644
index 0000000..8b1e323
--- /dev/null
+++ b/src/backing/containers/sift_result.rs
@@ -0,0 +1,26 @@
+use std::fmt::{Display, Formatter, Result as fmtResult};
+
+/// Indicates why a sift failed
+#[derive(Debug, Clone)]
+pub struct SiftError {
+    /// The index that couldn't be sifted
+    index: usize,
+    /// The length of the array
+    len: usize,
+}
+
+impl SiftError {
+    /// Instantiates a `SiftError`
+    pub fn new(index: usize, len: usize) -> Self {
+        Self { index, len }
+    }
+}
+
+impl Display for SiftError {
+    fn fmt(&self, f: &mut Formatter) -> fmtResult {
+        write!(f, "Could not sift index {} of {}", self.index, self.len)
+    }
+}
+
+/// Whether a sift operation succeeded
+pub type SiftResult = Result<(), SiftError>;
diff --git a/src/backing/indexed/binary_heap.rs b/src/backing/indexed/binary_heap.rs
index 84415ec..2f5dbc6 100644
--- a/src/backing/indexed/binary_heap.rs
+++ b/src/backing/indexed/binary_heap.rs
@@ -1,49 +1,194 @@
 use std::{collections::HashMap, hash::Hash};
 
-use crate::backing::{containers::Pair, indexed::IndexedBacking};
+use crate::backing::{
+    containers::{Pair, SiftError, SiftResult},
+    indexed::IndexedBacking,
+};
 
-pub struct IndexedBinaryHeap<D: Hash + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> {
+pub struct IndexedBinaryHeap<
+    D: Hash + Eq + Clone + Send + Sync,
+    P: PartialOrd + Clone + Send + Sync,
+> {
     data: Vec<Pair<D, P>>,
     indices: HashMap<D, usize>,
 }
 
-impl<D: Hash + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> IndexedBinaryHeap<D, P> {
+impl<D: Hash + Eq + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync>
+    IndexedBinaryHeap<D, P>
+{
     pub fn new() -> Self {
         Self {
             data: Vec::new(),
             indices: HashMap::new(),
         }
     }
+
+    fn sift_up(&mut self, i: usize) -> SiftResult {
+        print!("{i}");
+        if i == 0 {
+            // Base case, at root so nothing to do
+            Ok(())
+        } else if let Some(child) = self.data.get(i).cloned() {
+            let parent_index = (i - 1) / 2;
+            // Check if the heap property is violated
+            if child < self.data[parent_index] {
+                (self.data[i], self.data[parent_index]) =
+                    (self.data[parent_index].clone(), self.data[i].clone());
+                self.indices.insert(self.data[i].clone().data(), i).unwrap();
+                self.indices
+                    .insert(self.data[parent_index].clone().data(), parent_index)
+                    .unwrap();
+                self.sift_up(parent_index)
+            } else {
+                // Sift complete
+                Ok(())
+            }
+        } else {
+            // Tried to sift a non-existent index
+            Err(SiftError::new(i, self.data.len()))
+        }
+    }
+
+    fn sift_down(&mut self, i: usize) -> SiftResult {
+        print!("{i}");
+        if i > self.data.len() {
+            // Tried to sift a non-existent index
+            Err(SiftError::new(i, self.data.len()))
+        } else {
+            if let Some(first_child) = self.data.get(i * 2 + 1).cloned() {
+                let smaller_child_index;
+                let smaller_child;
+
+                // Find the smallest child and its index
+                if let Some(second_child) = self.data.get(i * 2 + 2).cloned() {
+                    // Both children, use the smaller one
+                    if first_child < second_child {
+                        smaller_child = first_child;
+                        smaller_child_index = i * 2 + 1;
+                    } else {
+                        smaller_child = second_child;
+                        smaller_child_index = i * 2 + 2;
+                    }
+                } else {
+                    // Only one child, no choice
+                    smaller_child = first_child;
+                    smaller_child_index = i * 2 + 1;
+                }
+
+                if smaller_child < self.data[i] {
+                    // Swap parent with child
+                    self.data[smaller_child_index] = self.data[i].clone();
+                    self.indices
+                        .insert(
+                            self.data[smaller_child_index].clone().data(),
+                            smaller_child_index,
+                        )
+                        .unwrap();
+                    self.data[i] = smaller_child.clone();
+                    self.indices.insert(smaller_child.data(), i).unwrap();
+
+                    // Repeat process with child
+                    self.sift_down(smaller_child_index)
+                } else {
+                    // Heap property satisfied, we're done
+                    Ok(())
+                }
+            } else {
+                // Base case, no children so nothing to do
+                Ok(())
+            }
+        }
+    }
+
+    fn delete_pair(&mut self, i: usize) -> Option<Pair<D, P>> {
+        if i >= self.data.len() {
+            return None;
+        }
+        let pair = self.data[i].clone();
+        if i < self.data.len() - 1 {
+            self.data[i] = self.data.pop().unwrap();
+            if self.data[i] < pair {
+                self.sift_up(i).unwrap();
+            } else {
+                self.sift_down(i).unwrap();
+            }
+        } else {
+            self.data.pop().unwrap();
+        }
+        self.indices.remove(pair.get_data()).unwrap();
+        Some(pair)
+    }
 }
 
-impl<D: Hash + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> FromIterator<(D, P)>
+impl<D: Hash + Eq + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> FromIterator<(D, P)>
     for IndexedBinaryHeap<D, P>
 {
     fn from_iter<T: IntoIterator<Item = (D, P)>>(iter: T) -> Self {
-        todo!()
+        let mut this = Self::new();
+        for (i, (data, priority)) in iter.into_iter().enumerate() {
+            if let Some(prev) = this.indices.insert(data.clone(), i) {
+                this.indices.insert(data.clone(), prev).unwrap();
+                this.data[prev] = Pair::new(data, priority);
+            } else {
+                this.data.push(Pair::new(data, priority));
+            }
+        }
+        for i in (0..=(this.data.len() / 2)).rev() {
+            this.sift_down(i).expect("Index error during heapify");
+        }
+        this
     }
 }
 
-impl<D: Hash + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> IndexedBacking<D, P>
+impl<D: Hash + Eq + Clone + Send + Sync, P: PartialOrd + Clone + Send + Sync> IndexedBacking<D, P>
     for IndexedBinaryHeap<D, P>
 {
     fn len(&self) -> usize {
-        todo!()
+        self.data.len()
     }
 
     fn contains(&self, data: &D) -> bool {
-        todo!()
+        self.indices.contains_key(data)
     }
 
     fn set(&mut self, data: D, priority: P) {
-        todo!()
+        if let Some(index) = self.indices.get(&data) {
+            let pair = self.data.get_mut(*index).unwrap();
+            let old_priority = pair.get_priority();
+            if priority < *old_priority {
+                pair.set_priority(priority);
+                self.sift_up(*index).unwrap();
+            } else {
+                pair.set_priority(priority);
+                self.sift_down(*index).unwrap();
+            }
+        } else {
+            let final_index = self.data.len();
+            if let Some(_) = self.indices.insert(data.clone(), final_index) {
+                panic!("Item was not consistently hashed")
+            }
+            self.data.push(Pair::new(data, priority));
+            self.sift_up(final_index).unwrap();
+        }
     }
 
     fn remove(&mut self, data: D) -> Option<P> {
-        todo!()
+        if let Some(index) = self.indices.get(&data) {
+            if let Some(pair) = self.delete_pair(*index) {
+                Some(pair.get_priority().clone())
+            } else {
+                None
+            }
+        } else {
+            None
+        }
     }
 
     fn pop(&mut self) -> Option<D> {
-        todo!()
+        if let Some(pair) = self.delete_pair(0) {
+            Some(pair.data())
+        } else {
+            None
+        }
     }
 }
diff --git a/src/backing/pure/binary_heap.rs b/src/backing/pure/binary_heap.rs
index cd84f18..2b43ec0 100644
--- a/src/backing/pure/binary_heap.rs
+++ b/src/backing/pure/binary_heap.rs
@@ -1,32 +1,7 @@
-use std::fmt;
+use crate::backing::containers::{SiftError, SiftResult};
 
 use super::PureBacking;
 
-/// Indicates why a sift failed
-#[derive(Debug, Clone)]
-struct SiftError {
-    /// The index that couldn't be sifted
-    index: usize,
-    /// The length of the array
-    len: usize,
-}
-
-impl SiftError {
-    /// Instantiates a `SiftError`
-    fn new(index: usize, len: usize) -> Self {
-        Self { index, len }
-    }
-}
-
-impl fmt::Display for SiftError {
-    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "Could not sift index {} of {}", self.index, self.len)
-    }
-}
-
-/// Whether a sift operation succeeded
-type SiftResult = Result<(), SiftError>;
-
 /// A binary min-heap backed by an array
 #[derive(Debug)]
 pub struct BinaryHeap<T: PartialOrd + Clone + Send + Sync> {