diff --git a/umap/umap_.py b/umap/umap_.py
index b6890734..0a4a4fd1 100644
--- a/umap/umap_.py
+++ b/umap/umap_.py
@@ -371,6 +371,18 @@ def make_tree(data, indices, rng_state, leaf_size=30, angular=False):
 
 
 def get_leaves(tree):
+    """Return the set of leaf nodes of a random projection tree.
+
+    Parameters
+    ----------
+    tree: RandomProjectionTreeNode
+        The root node of the tree to get leaves of.
+
+    Returns
+    -------
+    leaves: list
+        A list of arrays of indices of points in each leaf node.
+    """
     if tree.is_leaf:
         return [tree.indices]
     else:
@@ -379,6 +391,27 @@ def get_leaves(tree):
 
 @numba.njit('f8[:, :, :](i8,i8)')
 def make_heap(n_points, size):
+    """Constructor for the numba enabled heap objects. The heaps are used
+    for approximate nearest neighbor search, maintaining a list of potential
+    neighbors sorted by their distance. We also flag if potential neighbors
+    are newly added to the list or not. Internally this is stored as
+    a single ndarray; the first axis determines whether we are looking at the
+    array of candidate indices, the array of distances, or the flag array for
+    whether elements are new or not. Each of these arrays are of shape
+    (``n_points``, ``size``)
+
+    Parameters
+    ----------
+    n_points: int
+        The number of data points to track in the heap.
+
+    size: int
+        The number of items to keep on the heap for each data point.
+
+    Returns
+    -------
+    heap: An ndarray suitable for passing to other numba enabled heap functions.
+    """
     result = np.zeros((3, n_points, size))
     result[0] = -1
     result[1] = np.infty
@@ -389,6 +422,33 @@ def make_heap(n_points, size):
 
 @numba.jit('i8(f8[:,:,:],i8,f8,i8,i8)')
 def heap_push(heap, row, weight, index, flag):
+    """Push a new element onto the heap. The heap stores potential neighbors
+    for each data point. The ``row`` parameter determines which data point we
+    are addressing, the ``weight`` determines the distance (for heap sorting),
+    the ``index`` is the element to add, and the flag determines whether this
+    is to be considered a new addition.
+
+    Parameters
+    ----------
+    heap: ndarray generated by ``make_heap``
+        The heap object to push into
+
+    row: int
+        Which actual heap within the heap object to push to
+
+    weight: float
+        The priority value of the element to push onto the heap
+
+    index: int
+        The actual value to be pushed
+
+    flag: int
+        Whether to flag the newly added element or not.
+
+    Returns
+    -------
+    success: The number of new elements successfully pushed into the heap.
+    """
     indices = heap[0, row]
     weights = heap[1, row]
     is_new = heap[2, row]
@@ -396,6 +456,7 @@ def heap_push(heap, row, weight, index, flag):
     if weight > weights[0]:
         return 0
 
+    # break if we already have this element.
     for i in range(indices.shape[0]):
         if index == indices[i]:
             return 0