--- a/mercurial/configitems.py	Wed Sep 25 12:57:11 2019 +0200
+++ b/mercurial/configitems.py	Wed Sep 25 12:59:26 2019 +0200
@@ -645,6 +645,9 @@
 coreconfigitem('experimental', 'single-head-per-branch',
     default=False,
 )
+coreconfigitem('experimental', 'single-head-per-branch:account-closed-heads',
+    default=False,
+)
 coreconfigitem('experimental', 'sshserver.support-v2',
     default=False,
 )

--- a/mercurial/localrepo.py	Wed Sep 25 12:57:11 2019 +0200
+++ b/mercurial/localrepo.py	Wed Sep 25 12:59:26 2019 +0200
@@ -1920,8 +1920,13 @@
             # gating.
             tracktags(tr2)
             repo = reporef()
-            if repo.ui.configbool('experimental', 'single-head-per-branch'):
-                scmutil.enforcesinglehead(repo, tr2, desc)
+
+            r = repo.ui.configsuboptions('experimental',
+                                         'single-head-per-branch')
+            singlehead, singleheadsub = r
+            if singlehead:
+                accountclosed = singleheadsub.get("account-closed-heads", False)
+                scmutil.enforcesinglehead(repo, tr2, desc, accountclosed)
             if hook.hashook(repo.ui, 'pretxnclose-bookmark'):
                 for name, (old, new) in sorted(tr.changes['bookmarks'].items()):
                     args = tr.hookargs.copy()

--- a/mercurial/scmutil.py	Wed Sep 25 12:57:11 2019 +0200
+++ b/mercurial/scmutil.py	Wed Sep 25 12:59:26 2019 +0200
@@ -1895,14 +1895,16 @@
     first = ' '.join(short(h) for h in nodes[:maxnumnodes])
     return _("%s and %d others") % (first, len(nodes) - maxnumnodes)
 
-def enforcesinglehead(repo, tr, desc):
+def enforcesinglehead(repo, tr, desc, accountclosed=False):
     """check that no named branch has multiple heads"""
     if desc in ('strip', 'repair'):
         # skip the logic during strip
         return
     visible = repo.filtered('visible')
     # possible improvement: we could restrict the check to affected branch
-    for name, heads in visible.branchmap().iteritems():
+    bm = visible.branchmap()
+    for name in bm:
+        heads = bm.branchheads(name, closed=accountclosed)
         if len(heads) > 1:
             msg = _('rejecting multiple heads on branch "%s"')
             msg %= name

--- a/tests/test-single-head.t	Wed Sep 25 12:57:11 2019 +0200
+++ b/tests/test-single-head.t	Wed Sep 25 12:59:26 2019 +0200
@@ -200,3 +200,62 @@
   $ hg strip --config extensions.strip= --rev 'desc("c_dH0")'
   saved backup bundle to $TESTTMP/client/.hg/strip-backup/fe47ea669cea-a41bf5a9-backup.hg
 
+Test that closing heads are ignored by default
+-----------------------------------------------
+
+  $ hg up 'desc("c_aG0")'
+  0 files updated, 0 files merged, 2 files removed, 0 files unresolved
+  $ mkcommit c_aJ0
+  created new head
+
+pushing the new head should fails
+
+  $ hg push -f
+  pushing to $TESTTMP/single-head-server
+  searching for changes
+  adding changesets
+  adding manifests
+  adding file changes
+  transaction abort!
+  rollback completed
+  abort: rejecting multiple heads on branch "branch_A"
+  (2 heads: 49003e504178 468bd81ccc5d)
+  [255]
+
+
+closing the head and pushing should succeed
+
+  $ mkcommit c_aK0 --close-branch
+  $ hg push -f
+  pushing to $TESTTMP/single-head-server
+  searching for changes
+  adding changesets
+  adding manifests
+  adding file changes
+  added 4 changesets with 4 changes to 4 files (-1 heads)
+
+
+Test that closing heads can be explicitly accounted for
+-------------------------------------------------------
+
+  $ cat <<EOF >> $TESTTMP/single-head-server/.hg/hgrc
+  > [experimental]
+  > single-head-per-branch:account-closed-heads = yes
+  > EOF
+
+  $ hg up 'desc("c_aG0")'
+  0 files updated, 0 files merged, 2 files removed, 0 files unresolved
+  $ mkcommit c_aL0
+  created new head
+  $ mkcommit c_aM0 --close-branch
+  $ hg push -f
+  pushing to $TESTTMP/single-head-server
+  searching for changes
+  adding changesets
+  adding manifests
+  adding file changes
+  transaction abort!
+  rollback completed
+  abort: rejecting multiple heads on branch "branch_A"
+  (3 heads: 49003e504178 5254bcccab93 42b9fe70a3c1)
+  [255]