diff --git a/hgext/convert/subversion.py b/hgext/convert/subversion.py
--- a/hgext/convert/subversion.py
+++ b/hgext/convert/subversion.py
@@ -563,11 +563,15 @@ class svn_source(converter_source):
         reported. Return None if computed module does not belong to
         rootmodule subtree.
         """
-        def findchanges(path, start, stop):
-            stream = self._getlog([path], start, stop)
+        def findchanges(path, start, stop=None):
+            stream = self._getlog([path], start, stop or 1)
             try:
                 for entry in stream:
                     paths, revnum, author, date, message = entry
+                    if stop is None and paths:
+                        # We do not know the latest changed revision,
+                        # keep the first one with changed paths.
+                        break
                     if revnum <= stop:
                         break
 
@@ -580,6 +584,8 @@ class svn_source(converter_source):
                                       (path, newpath, revnum))
                         path = newpath
                         break
+                if not paths:
+                    revnum = None
                 return revnum, path
             finally:
                 stream.close()
@@ -605,6 +611,19 @@ class svn_source(converter_source):
         # development, but it might be in *another module*. Fetch the
         # log and detect renames down to the latest revision.
         revnum, realpath = findchanges(path, stop, dirent.created_rev)
+        if revnum is None:
+            # Tools like svnsync can create empty revision, when
+            # synchronizing only a subtree for instance. These empty
+            # revisions created_rev still have their original values
+            # despite all changes having disappeared and can be
+            # returned by ra.stat(), at least when stating the root
+            # module. In that case, do not trust created_rev and scan
+            # the whole history.
+            revnum, realpath = findchanges(path, stop)
+            if revnum is None:
+                self.ui.debug('ignoring empty branch %r\n' % realpath)
+                return None
+
         if not realpath.startswith(self.rootmodule):
             self.ui.debug('ignoring foreign branch %r\n' % realpath)
             return None
diff --git a/tests/svn/empty.svndump b/tests/svn/empty.svndump
new file mode 100644
--- /dev/null
+++ b/tests/svn/empty.svndump
@@ -0,0 +1,129 @@
+SVN-fs-dump-format-version: 2
+
+UUID: b70c45d5-2b76-4722-a373-d9babae61626
+
+Revision-number: 0
+Prop-content-length: 260
+Content-length: 260
+
+K 8
+svn:date
+V 27
+2012-04-18T11:35:14.752409Z
+K 17
+svn:sync-from-url
+V 73
+file:///Users/pmezard/dev/hg/hg-pmezard/tests/svn/temp/svn-repo/trunk/dir
+K 18
+svn:sync-from-uuid
+V 36
+56625b9e-e7e9-45be-ab61-052d41f0e1dd
+K 24
+svn:sync-last-merged-rev
+V 1
+4
+PROPS-END
+
+Revision-number: 1
+Prop-content-length: 112
+Content-length: 112
+
+K 10
+svn:author
+V 7
+pmezard
+K 8
+svn:date
+V 27
+2012-04-18T11:35:14.769622Z
+K 7
+svn:log
+V 10
+init projA
+PROPS-END
+
+Node-path: trunk
+Node-kind: dir
+Node-action: add
+Prop-content-length: 10
+Content-length: 10
+
+PROPS-END
+
+
+Revision-number: 2
+Prop-content-length: 107
+Content-length: 107
+
+K 10
+svn:author
+V 7
+pmezard
+K 8
+svn:date
+V 27
+2012-04-18T11:35:15.052989Z
+K 7
+svn:log
+V 6
+adddir
+PROPS-END
+
+Node-path: trunk/dir
+Node-kind: dir
+Node-action: add
+Prop-content-length: 10
+Content-length: 10
+
+PROPS-END
+
+
+Node-path: trunk/dir/a
+Node-kind: file
+Node-action: add
+Prop-content-length: 10
+Text-content-length: 2
+Text-content-md5: 60b725f10c9c85c70d97880dfe8191b3
+Text-content-sha1: 3f786850e387550fdab836ed7e6dc881de23001b
+Content-length: 12
+
+PROPS-END
+a
+
+
+Revision-number: 3
+Prop-content-length: 105
+Content-length: 105
+
+K 10
+svn:author
+V 7
+pmezard
+K 8
+svn:date
+V 27
+2012-04-18T11:35:16.050353Z
+K 7
+svn:log
+V 4
+addb
+PROPS-END
+
+Revision-number: 4
+Prop-content-length: 105
+Content-length: 105
+
+K 10
+svn:author
+V 7
+pmezard
+K 8
+svn:date
+V 27
+2012-04-18T11:35:17.050768Z
+K 7
+svn:log
+V 4
+addc
+PROPS-END
+
diff --git a/tests/svn/svndump-empty.sh b/tests/svn/svndump-empty.sh
new file mode 100755
--- /dev/null
+++ b/tests/svn/svndump-empty.sh
@@ -0,0 +1,47 @@
+#!/bin/sh
+#
+# Use this script to generate empty.svndump
+#
+
+mkdir temp
+cd temp
+
+mkdir project-orig
+cd project-orig
+mkdir trunk
+mkdir branches
+mkdir tags
+cd ..
+
+svnadmin create svn-repo
+svnurl=file://`pwd`/svn-repo
+svn import project-orig $svnurl -m "init projA"
+
+svn co $svnurl project
+cd project
+mkdir trunk/dir
+echo a > trunk/dir/a
+svn add trunk/dir
+svn ci -m adddir
+
+echo b > trunk/b
+svn add trunk/b
+svn ci -m addb
+
+echo c > c
+svn add c
+svn ci -m addc
+cd ..
+
+# svnsync repo/trunk/dir only so the last two revisions are empty
+svnadmin create svn-empty
+cat > svn-empty/hooks/pre-revprop-change <<EOF
+#!/bin/sh
+exit 0
+EOF
+chmod +x svn-empty/hooks/pre-revprop-change
+svnsync init --username svnsync file://`pwd`/svn-empty file://`pwd`/svn-repo/trunk/dir
+svnsync sync file://`pwd`/svn-empty
+svn log -v file://`pwd`/svn-empty
+
+svnadmin dump svn-empty > ../empty.svndump
diff --git a/tests/test-convert-svn-source.t b/tests/test-convert-svn-source.t
--- a/tests/test-convert-svn-source.t
+++ b/tests/test-convert-svn-source.t
@@ -187,3 +187,24 @@ This is also the only place testing more
   extra:       branch=default
   extra:       convert_revision=svn:........-....-....-....-............/proj B/mytrunk@1 (re)
   $ cd ..
+
+Test converting empty heads (issue3347)
+
+  $ svnadmin create svn-empty
+  $ svnadmin load -q svn-empty < "$TESTDIR/svn/empty.svndump"
+  $ hg --config convert.svn.trunk= convert svn-empty
+  assuming destination svn-empty-hg
+  initializing destination svn-empty-hg repository
+  scanning source...
+  sorting...
+  converting...
+  1 init projA
+  0 adddir
+  $ hg --config convert.svn.trunk= convert file://$svnpath/svn-empty/trunk
+  assuming destination trunk-hg
+  initializing destination trunk-hg repository
+  scanning source...
+  sorting...
+  converting...
+  1 init projA
+  0 adddir