diff --git a/xtas/tasks/pipeline.py b/xtas/tasks/pipeline.py
index 2a7f35d..2f871b9 100644
--- a/xtas/tasks/pipeline.py
+++ b/xtas/tasks/pipeline.py
@@ -3,6 +3,7 @@
 """
 
 import celery
+import warnings
 
 from xtas.tasks.es import is_es_document, es_address
 from xtas.tasks.es import get_single_result, store_single, fetch
@@ -12,44 +13,66 @@
 def pipeline(doc, pipeline, store_final=True, store_intermediate=False,
              block=True):
     """
-    Get the result for a given document.
-    Pipeline should be a list of dicts, with members task and argument
-    e.g. [{"module" : "tokenize"},
-          {"module" : "pos_tag", "arguments" : {"model" : "nltk"}}]
-    @param block: if True, it will block and return the actual result.
-                  If False, it will return an AsyncResult unless the result was
-                  cached, in which case it returns the result immediately (!)
-    @param store_final: if True, store the final result
-    @param store_intermediate: if True, store all intermediate results as well
+    Apply a sequence of operations to a document and return the result.
+
+    Parameters
+    ----------
+    doc : es_document or string
+        The document to process, either as a string, or a result of es_document().
+
+    pipeline : list of dicts
+        A list of dicts, each with members "task" and "arguments", e.g.
+        [{"task" : "tokenize"},
+         {"task" : "pos_tag", "arguments" : {"model" : "nltk"}}]
+        Using "module" instead of "task" is now obsolete, but still supported.
+
+    store_final : bool
+        If True, store the final result in ElasticSearch.
+
+    store_intermediate : bool
+        If True, store all intermediate results as well.
+
+    block : bool
+        If True, block, and return the result when it arrives.
+        If False, return the result directly if it's available immediately,
+        otherwise return an AsyncResult.
     """
-    # form basic pipeline by resolving task dictionaries to task objects
-    tasks = [_get_task(t) for t in pipeline]
 
+    tasks = [_get_task(t) for t in pipeline]
     if is_es_document(doc):
         idx, typ, id, field = es_address(doc)
-        chain = []
-        input = None
-        # Check cache for existing documents
-        # Iterate over tasks in reverse order, check cached result, and
-        # otherwise prepend task (and cache store command) to chain
-        for i in range(len(tasks), 0, -1):
-            taskname = "__".join(t.task for t in tasks[:i])
-            input = get_single_result(taskname, idx, typ, id)
-            if input:
+
+        def result_name(task_i):
+            "Results are named after the task that created them"
+            return "__".join(t.task for t in tasks[:(task_i + 1)])
+
+        last_cached_result = None
+        # we always have doc, which is result -1, the input to task 0
+        last_cached_i = -1
+        for task_i in reversed(range(0, len(tasks))):
+            last_cached_result = get_single_result(result_name(task_i),
+                                                   idx, typ, id)
+            if last_cached_result:
+                last_cached_i = task_i
                 break
-            if (i == len(tasks) and store_final) or store_intermediate:
-                chain.insert(0, store_single.s(taskname, idx, typ, id))
-            chain.insert(0, tasks[i-1])
-        if not chain:  # final result was cached, good!
-            return input
-        elif input is None:
-            input = fetch(doc)
-    else:
-        # the doc is a string, so we can't use caching
-        chain = tasks
-        input = doc
 
-    chain = celery.chain(*chain).delay(input)
+        if last_cached_i == -1:
+            doc = fetch(doc)
+        else:
+            doc = last_cached_result
+
+        new_tasks = []
+        for task_i in range(last_cached_i + 1, len(tasks)):
+            new_tasks.append(tasks[task_i])
+            if (task_i == len(tasks) and store_final) or store_intermediate:
+                new_tasks.append(store_single.s(result_name(task_i),
+                                                idx, typ, id))
+        tasks = new_tasks
+
+    if not tasks:
+        return doc
+
+    chain = celery.chain(*tasks).delay(doc)
     if block:
         return chain.get()
     else:
@@ -57,8 +80,12 @@ def pipeline(doc, pipeline, store_final=True, store_intermediate=False,
 
 
 def _get_task(task_dict):
-    "Create a celery task object from a dictionary with module and arguments"
-    task = task_dict['module']
+    "Create a celery task object from a dictionary with task name and arguments"
+    if 'task' not in task_dict and 'module' in task_dict:
+        warnings.warn('The "module" key is deprecated,'
+            ' please use "task" instead.', DeprecationWarning, stacklevel=2)
+        task_dict['task'] = task_dict['module']
+    task = task_dict['task']
     if isinstance(task, (str, unicode)):
         task = app.tasks[task]
     args = task_dict.get('arguments')
diff --git a/xtas/tests/test_pipeline.py b/xtas/tests/test_pipeline.py
index f06e512..ef58f79 100644
--- a/xtas/tests/test_pipeline.py
+++ b/xtas/tests/test_pipeline.py
@@ -33,12 +33,16 @@ def test_pipeline():
     assert_equal(result, expected)
     with eager_celery():
         # do we get correct result from pipeline?
+        r = pipeline(s, [{"task": tokenize},
+                         {"task": pos_tag, "arguments": {"model": "nltk"}}])
+        assert_equal(r, expected)
+        # is the old syntax still supported?
         r = pipeline(s, [{"module": tokenize},
                          {"module": pos_tag, "arguments": {"model": "nltk"}}])
         assert_equal(r, expected)
         # can we specify modules by name?
-        r = pipeline(s, [{"module": "xtas.tasks.single.tokenize"},
-                         {"module": "xtas.tasks.single.pos_tag",
+        r = pipeline(s, [{"task": "xtas.tasks.single.tokenize"},
+                         {"task": "xtas.tasks.single.pos_tag",
                           "arguments": {"model": "nltk"}}])
         assert_equal(r, expected)