diff --git a/anymail/backends/postmark.py b/anymail/backends/postmark.py
index 60c487b..2d2eeb9 100644
--- a/anymail/backends/postmark.py
+++ b/anymail/backends/postmark.py
@@ -183,8 +183,8 @@ class PostmarkPayload(RequestsPayload):
             if len(tags) > 1:
                 self.unsupported_feature('multiple tags (%r)' % tags)
 
-    # Postmark doesn't support click-tracking
-    # def set_track_clicks(self, track_clicks):
+    def set_track_clicks(self, track_clicks):
+        self.data["TrackLinks"] = 'HtmlAndText' if track_clicks else 'None'
 
     def set_track_opens(self, track_opens):
         self.data["TrackOpens"] = track_opens
diff --git a/docs/esps/index.rst b/docs/esps/index.rst
index dbb4e64..18643b6 100644
--- a/docs/esps/index.rst
+++ b/docs/esps/index.rst
@@ -34,7 +34,7 @@ Email Service Provider                        |Mailgun|   |Mandrill|  |Postmark|
 :attr:`~AnymailMessage.metadata`              Yes         Yes         No          Yes         Yes
 :attr:`~AnymailMessage.send_at`               Yes         Yes         No          Yes         Yes
 :attr:`~AnymailMessage.tags`                  Yes         Yes         Max 1 tag   Yes         Max 1 tag
-:attr:`~AnymailMessage.track_clicks`          Yes         Yes         No          Yes         Yes
+:attr:`~AnymailMessage.track_clicks`          Yes         Yes         Yes         Yes         Yes
 :attr:`~AnymailMessage.track_opens`           Yes         Yes         Yes         Yes         Yes
 
 .. rubric:: :ref:`templates-and-merge`
diff --git a/docs/esps/postmark.rst b/docs/esps/postmark.rst
index 83dbf49..14f5c9a 100644
--- a/docs/esps/postmark.rst
+++ b/docs/esps/postmark.rst
@@ -87,9 +87,7 @@ messages.)
 Limitations and quirks
 ----------------------
 
-Postmark has excellent support for standard email functionality, but does
-not support all the tracking and reporting additions offered by some other
-ESPs.
+Postmark does not support a few tracking and reporting additions offered by other ESPs.
 
 Anymail normally raises an :exc:`~anymail.exceptions.AnymailUnsupportedFeature`
 error when you try to send a message using features that Postmark doesn't support
@@ -107,13 +105,22 @@ see :ref:`unsupported-features`.
   Postmark does not support attaching :attr:`~anymail.message.AnymailMessage.metadata`
   to messages.
 
-**No click-tracking**
-  Postmark supports :attr:`~anymail.message.AnymailMessage.track_open`,
-  but not :attr:`~anymail.message.AnymailMessage.track_clicks`.
-
 **No delayed sending**
   Postmark does not support :attr:`~anymail.message.AnymailMessage.send_at`.
 
+**Click-tracking**
+  Postmark supports `several link-tracking options`_. Anymail treats
+  :attr:`~anymail.message.AnymailMessage.track_clicks` as Postmark's
+  "HtmlAndText" option when True.
+
+  If you would prefer Postmark's "HtmlOnly" or "TextOnly" link-tracking, you could
+  either set that as a Postmark server-level default (and use `message.track_clicks = False`
+  to disable tracking for specific messages), or use something like
+  `message.esp_extra = {'TrackLinks': "HtmlOnly"}` to specify a particular option.
+
+.. _several link-tracking options:
+   http://developer.postmarkapp.com/developer-link-tracking.html
+
 
 .. _postmark-templates:
 
diff --git a/tests/test_postmark_backend.py b/tests/test_postmark_backend.py
index 612ae34..7b2b383 100644
--- a/tests/test_postmark_backend.py
+++ b/tests/test_postmark_backend.py
@@ -325,8 +325,15 @@ class PostmarkBackendAnymailFeatureTests(PostmarkBackendMockAPITestCase):
 
     def test_track_clicks(self):
         self.message.track_clicks = True
-        with self.assertRaisesMessage(AnymailUnsupportedFeature, 'track_clicks'):
-            self.message.send()
+        self.message.send()
+        data = self.get_api_call_json()
+        self.assertEqual(data['TrackLinks'], 'HtmlAndText')
+
+        # Also explicit "None" for False (to override server default)
+        self.message.track_clicks = False
+        self.message.send()
+        data = self.get_api_call_json()
+        self.assertEqual(data['TrackLinks'], 'None')
 
     def test_template(self):
         self.message.template_id = 1234567
@@ -369,6 +376,7 @@ class PostmarkBackendAnymailFeatureTests(PostmarkBackendMockAPITestCase):
         self.assertNotIn('TemplateId', data)
         self.assertNotIn('TemplateModel', data)
         self.assertNotIn('TrackOpens', data)
+        self.assertNotIn('TrackLinks', data)
 
     def test_esp_extra(self):
         self.message.esp_extra = {
diff --git a/tests/test_postmark_integration.py b/tests/test_postmark_integration.py
index 871b566..05114bb 100644
--- a/tests/test_postmark_integration.py
+++ b/tests/test_postmark_integration.py
@@ -53,6 +53,7 @@ class PostmarkBackendIntegrationTests(SimpleTestCase, AnymailTestMixin):
             # no metadata, send_at, track_clicks support
             tags=["tag 1"],  # max one tag
             track_opens=True,
+            track_clicks=True,
         )
         message.attach("attachment1.txt", "Here is some\ntext for you", "text/plain")
         message.attach("attachment2.csv", "ID,Name\n1,Amy Lina", "text/csv")