diff --git a/mercurial/setdiscovery.py b/mercurial/setdiscovery.py
--- a/mercurial/setdiscovery.py
+++ b/mercurial/setdiscovery.py
@@ -275,9 +275,63 @@ def findcommonheads(ui, local, remote,
     # early exit if we know all the specified remote heads already
     ui.debug("query 1; heads\n")
     roundtrips += 1
-    sample = _limitsample(ownheads, initialsamplesize)
-    # indices between sample and externalized version must match
-    sample = list(sample)
+    # We also ask remote about all the local heads. That set can be arbitrarily
+    # large, so we used to limit it size to `initialsamplesize`. We no longer
+    # do as it proved counter productive. The skipped heads could lead to a
+    # large "undecided" set, slower to be clarified than if we asked the
+    # question for all heads right away.
+    #
+    # We are already fetching all server heads using the `heads` commands,
+    # sending a equivalent number of heads the other way should not have a
+    # significant impact.  In addition, it is very likely that we are going to
+    # have to issue "known" request for an equivalent amount of revisions in
+    # order to decide if theses heads are common or missing.
+    #
+    # find a detailled analysis below.
+    #
+    # Case A: local and server both has few heads
+    #
+    #     Ownheads is below initialsamplesize, limit would not have any effect.
+    #
+    # Case B: local has few heads and server has many
+    #
+    #     Ownheads is below initialsamplesize, limit would not have any effect.
+    #
+    # Case C: local and server both has many heads
+    #
+    #     We now transfert some more data, but not significantly more than is
+    #     already transfered to carry the server heads.
+    #
+    # Case D: local has many heads, server has few
+    #
+    #   D.1 local heads are mostly known remotely
+    #
+    #     All the known head will have be part of a `known` request at some
+    #     point for the discovery to finish. Sending them all earlier is
+    #     actually helping.
+    #
+    #     (This case is fairly unlikely, it requires the numerous heads to all
+    #     be merged server side in only a few heads)
+    #
+    #   D.2 local heads are mostly missing remotely
+    #
+    #     To determine that the heads are missing, we'll have to issue `known`
+    #     request for them or one of their ancestors. This amount of `known`
+    #     request will likely be in the same order of magnitude than the amount
+    #     of local heads.
+    #
+    #     The only case where we can be more efficient using `known` request on
+    #     ancestors are case were all the "missing" local heads are based on a
+    #     few changeset, also "missing".  This means we would have a "complex"
+    #     graph (with many heads) attached to, but very independant to a the
+    #     "simple" graph on the server. This is a fairly usual case and have
+    #     not been met in the wild so far.
+    if remote.limitedarguments:
+        sample = _limitsample(ownheads, initialsamplesize)
+        # indices between sample and externalized version must match
+        sample = list(sample)
+    else:
+        sample = ownheads
 
     with remote.commandexecutor() as e:
         fheads = e.callcommand('heads', {})
diff --git a/tests/test-setdiscovery.t b/tests/test-setdiscovery.t
--- a/tests/test-setdiscovery.t
+++ b/tests/test-setdiscovery.t
@@ -926,7 +926,7 @@ Both many new on top of long history:
   common heads: 7ead0cba2838
 
 
-One with >200 heads, which used to use up all of the sample:
+One with >200 heads. We now switch to send them all in the initial roundtrip, but still do sampling for the later request.
 
   $ hg init manyheads
   $ cd manyheads
@@ -974,20 +974,17 @@ One with >200 heads, which used to use u
   searching for changes
   taking quick initial sample
   searching: 2 queries
-  query 2; still undecided: 1240, sample size is: 100
+  query 2; still undecided: 1080, sample size is: 100
   sampling from both directions
   searching: 3 queries
-  query 3; still undecided: 1140, sample size is: 200
+  query 3; still undecided: 980, sample size is: 200
   sampling from both directions
   searching: 4 queries
   query 4; still undecided: \d+, sample size is: 200 (re)
   sampling from both directions
   searching: 5 queries
-  query 5; still undecided: \d+, sample size is: 200 (re)
-  sampling from both directions
-  searching: 6 queries
-  query 6; still undecided: \d+, sample size is: \d+ (re)
-  6 total queries in *.????s (glob)
+  query 5; still undecided: 195, sample size is: 195
+  5 total queries in *.????s (glob)
   elapsed time:  * seconds (glob)
   heads summary:
     total common heads:          1
@@ -1116,6 +1113,6 @@ fixed in 86c35b7ae300:
   $ hg -R r1 --config extensions.blackbox= blackbox --config blackbox.track=
   * @5d0b986a083e0d91f116de4691e2aaa54d5bbec0 (*)> serve --cmdserver chgunix * (glob) (chg !)
   * @5d0b986a083e0d91f116de4691e2aaa54d5bbec0 (*)> -R r1 outgoing r2 *-T{rev} * --config *extensions.blackbox=* (glob)
-  * @5d0b986a083e0d91f116de4691e2aaa54d5bbec0 (*)> found 101 common and 1 unknown server heads, 2 roundtrips in *.????s (glob)
+  * @5d0b986a083e0d91f116de4691e2aaa54d5bbec0 (*)> found 101 common and 1 unknown server heads, 1 roundtrips in *.????s (glob)
   * @5d0b986a083e0d91f116de4691e2aaa54d5bbec0 (*)> -R r1 outgoing r2 *-T{rev} * --config *extensions.blackbox=* exited 0 after *.?? seconds (glob)
   $ cd ..