diff --git a/mercurial/configitems.py b/mercurial/configitems.py
--- a/mercurial/configitems.py
+++ b/mercurial/configitems.py
@@ -176,6 +176,9 @@
 coreconfigitem('experimental', 'copytrace',
     default='on',
 )
+coreconfigitem('experimental', 'copytrace.sourcecommitlimit',
+    default=100,
+)
 coreconfigitem('experimental', 'crecordtest',
     default=None,
 )
diff --git a/mercurial/copies.py b/mercurial/copies.py
--- a/mercurial/copies.py
+++ b/mercurial/copies.py
@@ -371,22 +371,27 @@
         # Do full copytracing if only drafts are involved as that will be fast
         # enough and will also cover the copies which can be missed by
         # heuristics
-        if _isfullcopytraceable(c1, base):
+        if _isfullcopytraceable(repo, c1, base):
             return _fullcopytracing(repo, c1, c2, base)
         return _heuristicscopytracing(repo, c1, c2, base)
     else:
         return _fullcopytracing(repo, c1, c2, base)
 
-def _isfullcopytraceable(c1, base):
+def _isfullcopytraceable(repo, c1, base):
     """ Checks that if base, source and destination are all draft branches, if
     yes let's use the full copytrace algorithm for increased capabilities since
     it will be fast enough.
     """
+    if c1.rev() is None:
+        c1 = c1.p1()
 
     nonpublicphases = set([phases.draft, phases.secret])
 
     if (c1.phase() in nonpublicphases) and (base.phase() in nonpublicphases):
-        return True
+        sourcecommitlimit = repo.ui.configint('experimental',
+                                              'copytrace.sourcecommitlimit')
+        commits = len(repo.revs('%d::%d', base.rev(), c1.rev()))
+        return commits < sourcecommitlimit
     return False
 
 def _fullcopytracing(repo, c1, c2, base):
diff --git a/tests/test-copytrace-heuristics.t b/tests/test-copytrace-heuristics.t
--- a/tests/test-copytrace-heuristics.t
+++ b/tests/test-copytrace-heuristics.t
@@ -665,3 +665,50 @@
   dummy
   $ rm -rf server
   $ rm -rf repo
+
+Testing the sourcecommitlimit config
+
+  $ hg init repo
+  $ initclient repo
+  $ cd repo
+  $ echo a > a
+  $ hg ci -Aqm "added a"
+  $ echo "more things" >> a
+  $ hg ci -qm "added more things to a"
+  $ hg up 0
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ echo b > b
+  $ hg ci -Aqm "added b"
+  $ mkdir foo
+  $ hg mv a foo/bar
+  $ hg ci -m "Moved a to foo/bar"
+  $ hg log -G -T 'changeset {node}\n desc {desc}, phase: {phase}\n'
+  @  changeset b4b0f7880e500b5c364a5f07b4a2b167de7a6fb0
+  |   desc Moved a to foo/bar, phase: draft
+  o  changeset 5f6d8a4bf34ab274ccc9f631c2536964b8a3666d
+  |   desc added b, phase: draft
+  | o  changeset 8b6e13696c38e8445a759516474640c2f8dddef6
+  |/    desc added more things to a, phase: draft
+  o  changeset 9092f1db7931481f93b37d5c9fbcfc341bcd7318
+      desc added a, phase: draft
+
+When the sourcecommitlimit is small and we have more drafts, we use heuristics only
+
+  $ hg rebase -s 8b6e13696 -d . --config experimental.copytrace.sourcecommitlimit=0
+  rebasing 1:8b6e13696c38 "added more things to a"
+  other [source] changed a which local [dest] deleted
+  use (c)hanged version, leave (d)eleted, or leave (u)nresolved? u
+  unresolved conflicts (see hg resolve, then hg rebase --continue)
+  [1]
+
+But when we have "sourcecommitlimit > (no. of drafts from base to c1)", we do
+fullcopytracing
+
+  $ hg rebase --abort
+  rebase aborted
+  $ hg rebase -s 8b6e13696 -d .
+  rebasing 1:8b6e13696c38 "added more things to a"
+  merging foo/bar and a to foo/bar
+  saved backup bundle to $TESTTMP/repo/repo/repo/.hg/strip-backup/8b6e13696c38-fc14ac83-rebase.hg (glob)
+  $ cd ..
+  $ rm -rf repo