diff --git a/api-ref/source/parameters.yaml b/api-ref/source/parameters.yaml
index 8ab65f58ea..425366d049 100644
--- a/api-ref/source/parameters.yaml
+++ b/api-ref/source/parameters.yaml
@@ -692,18 +692,31 @@ X-Copy-From-Account:
   type: string
 X-Delete-After:
   description: |
-    The number of seconds after which the system
-    removes the object. Internally, the Object Storage system stores
-    this value in the ``X-Delete-At`` metadata item.
+    The number of seconds after which the system removes the object. The value
+    should be a positive integer. Internally, the Object Storage system uses
+    this value to generate an ``X-Delete-At`` metadata item. If both
+    ``X-Delete-After`` and ``X-Delete-At`` are set then ``X-Delete-After``
+    takes precedence.
   in: header
   required: false
   type: integer
 X-Delete-At:
   description: |
-    The date and time in `UNIX Epoch time stamp
-    format <https://en.wikipedia.org/wiki/Unix_time>`_ when the system
-    removes the object.  For example, ``1440619048`` is equivalent to
-    ``Mon, Wed, 26 Aug 2015 19:57:28 GMT``.
+    The date and time in `UNIX Epoch time stamp format
+    <https://en.wikipedia.org/wiki/Unix_time>`_ when the system removes the
+    object.  For example, ``1440619048`` is equivalent to ``Mon, Wed, 26 Aug
+    2015 19:57:28 GMT``.  The value should be a positive integer corresponding
+    to a time in the future. If both ``X-Delete-After`` and ``X-Delete-At`` are
+    set then ``X-Delete-After`` takes precedence.
+  in: header
+  required: false
+  type: integer
+X-Delete-At_resp:
+  description: |
+    If present, specifies date and time in `UNIX Epoch time stamp format
+    <https://en.wikipedia.org/wiki/Unix_time>`_ when the system removes the
+    object.  For example, ``1440619048`` is equivalent to ``Mon, Wed, 26 Aug
+    2015 19:57:28 GMT``.
   in: header
   required: false
   type: integer
diff --git a/api-ref/source/storage-object-services.inc b/api-ref/source/storage-object-services.inc
index 4c2b45b38f..96816997eb 100644
--- a/api-ref/source/storage-object-services.inc
+++ b/api-ref/source/storage-object-services.inc
@@ -130,7 +130,7 @@ Response Parameters
    - X-Object-Meta-name: X-Object-Meta-name_resp
    - Content-Disposition: Content-Disposition_resp
    - Content-Encoding: Content-Encoding_resp
-   - X-Delete-At: X-Delete-At
+   - X-Delete-At: X-Delete-At_resp
    - Accept-Ranges: Accept-Ranges
    - X-Object-Manifest: X-Object-Manifest_resp
    - Last-Modified: Last-Modified
@@ -602,7 +602,7 @@ Response Parameters
    - X-Object-Meta-name: X-Object-Meta-name
    - Content-Disposition: Content-Disposition_resp
    - Content-Encoding: Content-Encoding_resp
-   - X-Delete-At: X-Delete-At
+   - X-Delete-At: X-Delete-At_resp
    - X-Object-Manifest: X-Object-Manifest_resp
    - Last-Modified: Last-Modified
    - ETag: ETag_obj_resp
@@ -752,9 +752,9 @@ Request
    - X-Service-Token: X-Service-Token
    - X-Object-Meta-name: X-Object-Meta-name
    - X-Delete-At: X-Delete-At
+   - X-Delete-After: X-Delete-After
    - Content-Disposition: Content-Disposition
    - Content-Encoding: Content-Encoding
-   - X-Delete-After: X-Delete-After
    - Content-Type: Content-Type_obj_cu_req
    - X-Trans-Id-Extra: X-Trans-Id-Extra
 
diff --git a/doc/source/overview_expiring_objects.rst b/doc/source/overview_expiring_objects.rst
index 42942c8751..9d8c2d911d 100644
--- a/doc/source/overview_expiring_objects.rst
+++ b/doc/source/overview_expiring_objects.rst
@@ -11,9 +11,12 @@ object from the system.
 The ``X-Delete-At`` header takes a Unix Epoch timestamp, in integer form; for
 example: ``1317070737`` represents ``Mon Sep 26 20:58:57 2011 UTC``.
 
-The ``X-Delete-After`` header takes an integer number of seconds. The proxy
-server that receives the request will convert this header into an
-``X-Delete-At`` header using its current time plus the value given.
+The ``X-Delete-After`` header takes a positive integer number of seconds. The
+proxy server that receives the request will convert this header into an
+``X-Delete-At`` header using the request timestamp plus the value given.
+
+If both the ``X-Delete-At`` and ``X-Delete-After`` headers are sent with a
+request then the ``X-Delete-After`` header will take precedence.
 
 As expiring objects are added to the system, the object servers will record the
 expirations in a hidden ``.expiring_objects`` account for the