diff --git a/docs/source/active_memory_manager.rst b/docs/source/active_memory_manager.rst
index 3fd5a68f238..40d2be643df 100644
--- a/docs/source/active_memory_manager.rst
+++ b/docs/source/active_memory_manager.rst
@@ -7,8 +7,9 @@ usage of workers across the Dask cluster. It is disabled by default.
 Memory imbalance and duplication
 --------------------------------
 Whenever a Dask task returns data, it is stored on the worker that executed the task for
-as long as it's a dependency of other tasks, is referenced by a ``Client`` through a
-``Future``, or is part of a :doc:`published dataset <publish>`.
+as long as it's a dependency of other tasks, is referenced by a
+:class:`~distributed.Client` through a :class:`~distributed.Future`, or is part of a
+:doc:`published dataset <publish>`.
 
 Dask assigns tasks to workers following criteria of CPU occupancy, :doc:`resources`, and
 locality. In the trivial use case of tasks that are not connected to each other, take
@@ -38,7 +39,7 @@ The AMM can be enabled through the :doc:`Dask configuration file <configuration>
 
 The above is the recommended setup and will run all enabled *AMM policies* (see below)
 every two seconds. Alternatively, you can manually start/stop the AMM from the
-``Client`` or trigger a one-off iteration:
+:class:`~distributed.`Client` or trigger a one-off iteration:
 
 .. code-block:: python
 
@@ -58,6 +59,10 @@ long as they don't harm data integrity. These suggestions can be of two types:
 - Delete one or more replicas of an in-memory task. The AMM will never delete the last
   replica of a task, even if a policy asks to.
 
+There are no "move" operations. A move is performed in two passes: first a policy
+creates a copy; in the next AMM iteration, the same or another policy deletes the
+original (if the copy succeeded).
+
 Unless a policy puts constraints on which workers should be impacted, the AMM will
 automatically create replicas on workers with the lowest memory usage first and delete
 them from workers with the highest memory usage first.
@@ -90,7 +95,7 @@ Built-in policies
 ReduceReplicas
 ++++++++++++++
 class
-    ``distributed.active_memory_manager.ReduceReplicas``
+    :class:`distributed.active_memory_manager.ReduceReplicas`
 parameters
     None
 
@@ -128,7 +133,7 @@ define two methods:
         Create one replica of the target task on the worker with the lowest memory among
         the listed candidates.
     ``yield "drop", <TaskState>, None``
-        Delete one replica of the target task one the worker with the highest memory
+        Delete one replica of the target task on the worker with the highest memory
         usage across the whole cluster.
     ``yield "drop", <TaskState>, {<WorkerState>, <WorkerState>, ...}``
         Delete one replica of the target task on the worker with the highest memory
@@ -186,8 +191,8 @@ Example
 The following custom policy ensures that keys "foo" and "bar" are replicated on all
 workers at all times. New workers will receive a replica soon after connecting to the
 scheduler. The policy will do nothing if the target keys are not in memory somewhere or
-if all workers already hold a replica.
-Note that this example is incompatible with the ``ReduceReplicas`` built-in policy.
+if all workers already hold a replica. Note that this example is incompatible with the
+:class:`~distributed.active_memory_manager.ReduceReplicas built-in policy.
 
 In mymodule.py (it must be accessible by the scheduler):