diff --git a/hgext/convert/filemap.py b/hgext/convert/filemap.py
--- a/hgext/convert/filemap.py
+++ b/hgext/convert/filemap.py
@@ -294,23 +294,34 @@ class filemap_source(converter_source):
         # A parent p is interesting if its mapped version (self.parentmap[p]):
         # - is not SKIPREV
         # - is still not in the list of parents (we don't want duplicates)
-        # - is not an ancestor of the mapped versions of the other parents
+        # - is not an ancestor of the mapped versions of the other parents or
+        #   there is no parent in the same branch than the current revision.
         mparents = []
-        wp = None
+        knownparents = set()
+        branch = self.commits[rev].branch
+        hasbranchparent = False
         for i, p1 in enumerate(parents):
             mp1 = self.parentmap[p1]
-            if mp1 == SKIPREV or mp1 in mparents:
+            if mp1 == SKIPREV or mp1 in knownparents:
                 continue
-            for p2 in parents:
-                if p1 == p2 or mp1 == self.parentmap[p2]:
-                    continue
-                if mp1 in self.wantedancestors[p2]:
-                    break
-            else:
-                mparents.append(mp1)
-                wp = i
-
-        if wp is None and parents:
+            isancestor = util.any(p2 for p2 in parents
+                                  if p1 != p2 and mp1 != self.parentmap[p2]
+                                  and mp1 in self.wantedancestors[p2])
+            if not isancestor and not hasbranchparent and len(parents) > 1:
+                # This could be expensive, avoid unnecessary calls.
+                if self._cachedcommit(p1).branch == branch:
+                    hasbranchparent = True
+            mparents.append((p1, mp1, i, isancestor))
+            knownparents.add(mp1)
+        # Discard parents ancestors of other parents if there is a
+        # non-ancestor one on the same branch than current revision.
+        if hasbranchparent:
+            mparents = [p for p in mparents if not p[3]]
+        wp = None
+        if mparents:
+            wp = max(p[2] for p in mparents)
+            mparents = [p[1] for p in mparents]
+        elif parents:
             wp = 0
 
         self.origparents[rev] = parents
@@ -319,7 +330,6 @@ class filemap_source(converter_source):
         if 'close' in self.commits[rev].extra:
             # A branch closing revision is only useful if one of its
             # parents belong to the branch being closed
-            branch = self.commits[rev].branch
             pbranches = [self._cachedcommit(p).branch for p in mparents]
             if branch in pbranches:
                 closed = True
diff --git a/tests/test-convert-filemap.t b/tests/test-convert-filemap.t
--- a/tests/test-convert-filemap.t
+++ b/tests/test-convert-filemap.t
@@ -375,3 +375,189 @@ exercise incremental conversion at the s
   |
   o  0 "addb" files: b
   
+
+test merge parents/empty merges pruning
+
+  $ glog()
+  > {
+  >     hg glog --template '{rev}:{node|short}@{branch} "{desc}" files: {files}\n' "$@"
+  > }
+
+test anonymous branch pruning
+
+  $ hg init anonymousbranch
+  $ cd anonymousbranch
+  $ echo a > a
+  $ echo b > b
+  $ hg ci -Am add
+  adding a
+  adding b
+  $ echo a >> a
+  $ hg ci -m changea
+  $ hg up 0
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ echo b >> b
+  $ hg ci -m changeb
+  created new head
+  $ hg up 1
+  2 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ hg merge
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  (branch merge, don't forget to commit)
+  $ hg ci -m merge
+  $ cd ..
+
+  $ cat > filemap <<EOF
+  > include a
+  > EOF
+  $ hg convert --filemap filemap anonymousbranch anonymousbranch-hg
+  initializing destination anonymousbranch-hg repository
+  scanning source...
+  sorting...
+  converting...
+  3 add
+  2 changea
+  1 changeb
+  0 merge
+  $ glog -R anonymousbranch
+  @    3:c71d5201a498@default "merge" files:
+  |\
+  | o  2:607eb44b17f9@default "changeb" files: b
+  | |
+  o |  1:1f60ea617824@default "changea" files: a
+  |/
+  o  0:0146e6129113@default "add" files: a b
+  
+  $ glog -R anonymousbranch-hg
+  o  1:cda818e7219b@default "changea" files: a
+  |
+  o  0:c334dc3be0da@default "add" files: a
+  
+  $ cat anonymousbranch-hg/.hg/shamap
+  0146e6129113dba9ac90207cfdf2d7ed35257ae5 c334dc3be0daa2a4e9ce4d2e2bdcba40c09d4916
+  1f60ea61782421edf8d051ff4fcb61b330f26a4a cda818e7219b5f7f3fb9f49780054ed6a1905ec3
+  607eb44b17f9348cd5cbd26e16af87ba77b0b037 c334dc3be0daa2a4e9ce4d2e2bdcba40c09d4916
+  c71d5201a498b2658d105a6bf69d7a0df2649aea cda818e7219b5f7f3fb9f49780054ed6a1905ec3
+
+  $ cat > filemap <<EOF
+  > include b
+  > EOF
+  $ hg convert --filemap filemap anonymousbranch anonymousbranch-hg2
+  initializing destination anonymousbranch-hg2 repository
+  scanning source...
+  sorting...
+  converting...
+  3 add
+  2 changea
+  1 changeb
+  0 merge
+  $ glog -R anonymousbranch
+  @    3:c71d5201a498@default "merge" files:
+  |\
+  | o  2:607eb44b17f9@default "changeb" files: b
+  | |
+  o |  1:1f60ea617824@default "changea" files: a
+  |/
+  o  0:0146e6129113@default "add" files: a b
+  
+  $ glog -R anonymousbranch-hg2
+  o  1:62dd350b0df6@default "changeb" files: b
+  |
+  o  0:4b9ced861657@default "add" files: b
+  
+  $ cat anonymousbranch-hg2/.hg/shamap
+  0146e6129113dba9ac90207cfdf2d7ed35257ae5 4b9ced86165703791653059a1db6ed864630a523
+  1f60ea61782421edf8d051ff4fcb61b330f26a4a 4b9ced86165703791653059a1db6ed864630a523
+  607eb44b17f9348cd5cbd26e16af87ba77b0b037 62dd350b0df695f7d2c82a02e0499b16fd790f22
+  c71d5201a498b2658d105a6bf69d7a0df2649aea 62dd350b0df695f7d2c82a02e0499b16fd790f22
+
+test named branch pruning
+
+  $ hg init namedbranch
+  $ cd namedbranch
+  $ echo a > a
+  $ echo b > b
+  $ hg ci -Am add
+  adding a
+  adding b
+  $ echo a >> a
+  $ hg ci -m changea
+  $ hg up 0
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ hg branch foo
+  marked working directory as branch foo
+  (branches are permanent and global, did you want a bookmark?)
+  $ echo b >> b
+  $ hg ci -m changeb
+  $ hg up default
+  2 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ hg merge foo
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  (branch merge, don't forget to commit)
+  $ hg ci -m merge
+  $ cd ..
+
+  $ cat > filemap <<EOF
+  > include a
+  > EOF
+  $ hg convert --filemap filemap namedbranch namedbranch-hg
+  initializing destination namedbranch-hg repository
+  scanning source...
+  sorting...
+  converting...
+  3 add
+  2 changea
+  1 changeb
+  0 merge
+  $ glog -R namedbranch
+  @    3:73899bcbe45c@default "merge" files:
+  |\
+  | o  2:8097982d19fc@foo "changeb" files: b
+  | |
+  o |  1:1f60ea617824@default "changea" files: a
+  |/
+  o  0:0146e6129113@default "add" files: a b
+  
+  $ glog -R namedbranch-hg
+  o  1:cda818e7219b@default "changea" files: a
+  |
+  o  0:c334dc3be0da@default "add" files: a
+  
+
+  $ cd namedbranch
+  $ hg --config extensions.mq= strip tip
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  saved backup bundle to $TESTTMP/namedbranch/.hg/strip-backup/73899bcbe45c-backup.hg
+  $ hg up foo
+  2 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  $ hg merge default
+  1 files updated, 0 files merged, 0 files removed, 0 files unresolved
+  (branch merge, don't forget to commit)
+  $ hg ci -m merge
+  $ cd ..
+
+  $ hg convert --filemap filemap namedbranch namedbranch-hg2
+  initializing destination namedbranch-hg2 repository
+  scanning source...
+  sorting...
+  converting...
+  3 add
+  2 changea
+  1 changeb
+  0 merge
+  $ glog -R namedbranch
+  @    3:e1959de76e1b@foo "merge" files:
+  |\
+  | o  2:8097982d19fc@foo "changeb" files: b
+  | |
+  o |  1:1f60ea617824@default "changea" files: a
+  |/
+  o  0:0146e6129113@default "add" files: a b
+  
+  $ glog -R namedbranch-hg2
+  o    2:dcf314454667@foo "merge" files:
+  |\
+  | o  1:cda818e7219b@default "changea" files: a
+  |/
+  o  0:c334dc3be0da@default "add" files: a
+