diff --git a/chest/core.py b/chest/core.py
index c1b1b31..a65ceb7 100644
--- a/chest/core.py
+++ b/chest/core.py
@@ -82,7 +82,7 @@ def __init__(self, data=None, path=None, available_memory=None,
         # In memory storage
         self.inmem = data or dict()
         # A set of keys held both in memory or on disk
-        self._keys = set()
+        self._keys = {}
         # Was a path given or no?  If not we'll clean up the directory later
         self._explicitly_given_path = path is not None
         # Diretory where the on-disk data will be held
@@ -101,7 +101,7 @@ def __init__(self, data=None, path=None, available_memory=None,
         keyfile = os.path.join(self.path, '.keys')
         if os.path.exists(keyfile):
             with open(keyfile, mode='r'+self.mode) as f:
-                self._keys = set(self.load(f))
+                self._keys = dict(self.load(f))
 
         self.lock = Lock()
 
@@ -123,7 +123,7 @@ def key_to_filename(self, key):
     def move_to_disk(self, key):
         """ Move data from memory onto disk """
         self._on_overflow(key)
-        fn = self.key_to_filename(key)
+        fn = self._keys[key]
         if not os.path.exists(fn):  # Only write if it doesn't exist.
             dir = os.path.dirname(fn)
             if not os.path.exists(dir):
@@ -143,7 +143,7 @@ def get_from_disk(self, key):
 
         self._on_miss(key)
 
-        fn = self.key_to_filename(key)
+        fn = self._keys[key]
         with open(fn, mode='r'+self.mode) as f:
             value = self.load(f)
 
@@ -176,11 +176,11 @@ def __delitem__(self, key):
         if key in self.heap:
             del self.heap[key]
 
-        fn = self.key_to_filename(key)
+        fn = self._keys[key]
         if os.path.exists(fn):
             os.remove(fn)
 
-        self._keys.remove(key)
+        del self._keys[key]
 
     def __setitem__(self, key, value):
         with self.lock:
@@ -188,7 +188,7 @@ def __setitem__(self, key, value):
                 del self[key]
 
             self.inmem[key] = value
-            self._keys.add(key)
+            self._keys[key] = self.key_to_filename(key)
             self._update_lru(key)
 
         with self.lock:
@@ -242,7 +242,7 @@ def drop(self):
     def write_keys(self):
         fn = os.path.join(self.path, '.keys')
         with open(fn, mode='w'+self.mode) as f:
-            self.dump(list(self._keys), f)
+            self.dump(list(self._keys.items()), f)
 
     def flush(self):
         """ Flush all in-memory storage to disk """
@@ -275,13 +275,13 @@ def update(self, other, overwrite=True):
                 del self[key]
             elif key in self._keys and not overwrite:
                 continue
-            old_fn = os.path.join(other.path, other._key_to_filename(key))
+            old_fn = other._keys[key]
             new_fn = os.path.join(self.path, self._key_to_filename(key))
             dir = os.path.dirname(new_fn)
             if not os.path.exists(dir):
                 os.makedirs(dir)
             os.link(old_fn, new_fn)
-            self._keys.add(key)
+            self._keys[key] = new_fn
 
 
 def nbytes(o):
diff --git a/chest/tests/test_core.py b/chest/tests/test_core.py
index e66003e..53bc27d 100644
--- a/chest/tests/test_core.py
+++ b/chest/tests/test_core.py
@@ -8,6 +8,7 @@
 import numpy as np
 from chest.utils import raises
 import time
+import hashlib
 
 
 @contextmanager
@@ -27,6 +28,11 @@ def tmp_chest(*args, **kwargs):
             pass
 
 
+def my_key_to_fname(key):
+    fname = str(hashlib.md5(str(key).encode()).hexdigest())
+    return fname
+
+
 def test_basic():
     with tmp_chest() as c:
         c[1] = 'one'
@@ -384,3 +390,13 @@ def test_nested_files_with_tuples():
         c['a', 'b', 'c', 'd', 'e'] = 5
         c.flush()
         assert c['a', 'b', 'c', 'd', 'e'] == 5
+
+
+def test_store_fnames():
+    with tmp_chest(key_to_filename=my_key_to_fname) as c1:
+        c1[('spam', 'eggs')] = 'spam and eggs'
+        c1.flush()
+        with tmp_chest() as c2:
+            c2.update(c1)
+            c2.flush()
+            assert c2[('spam', 'eggs')] == 'spam and eggs'