diff --git a/hgext/largefiles/overrides.py b/hgext/largefiles/overrides.py
--- a/hgext/largefiles/overrides.py
+++ b/hgext/largefiles/overrides.py
@@ -515,14 +515,16 @@ def overridecopy(orig, ui, repo, pats, o
                     dest.startswith(repo.wjoin(lfutil.shortname))):
                     srclfile = src.replace(repo.wjoin(lfutil.standin('')), '')
                     destlfile = dest.replace(repo.wjoin(lfutil.standin('')), '')
-                    destlfiledir = os.path.dirname(destlfile) or '.'
+                    destlfiledir = os.path.dirname(repo.wjoin(destlfile)) or '.'
                     if not os.path.isdir(destlfiledir):
                         os.makedirs(destlfiledir)
                     if rename:
                         os.rename(repo.wjoin(srclfile), repo.wjoin(destlfile))
                         lfdirstate.remove(srclfile)
                     else:
-                        util.copyfile(srclfile, destlfile)
+                        util.copyfile(repo.wjoin(srclfile),
+                                      repo.wjoin(destlfile))
+
                     lfdirstate.add(destlfile)
             lfdirstate.write()
         except util.Abort, e:
diff --git a/tests/test-largefiles.t b/tests/test-largefiles.t
--- a/tests/test-largefiles.t
+++ b/tests/test-largefiles.t
@@ -141,6 +141,43 @@ Test moving largefiles and verify that n
   $ cat sub/large4
   large22
 
+Test copies and moves from a directory other than root (issue3516)
+
+  $ cd ..
+  $ hg init lf_cpmv
+  $ cd lf_cpmv
+  $ mkdir dira
+  $ mkdir dira/dirb
+  $ touch dira/dirb/largefile
+  $ hg add --large dira/dirb/largefile
+  $ hg commit -m "added"
+  Invoking status precommit hook
+  A dira/dirb/largefile
+  $ cd dira
+  $ hg cp dirb/largefile foo/largefile
+  $ hg ci -m "deep copy"
+  Invoking status precommit hook
+  A dira/foo/largefile
+  $ find . | sort
+  .
+  ./dirb
+  ./dirb/largefile
+  ./foo
+  ./foo/largefile
+  $ hg mv foo/largefile baz/largefile
+  $ hg ci -m "moved"
+  Invoking status precommit hook
+  A dira/baz/largefile
+  R dira/foo/largefile
+  $ find . | sort
+  .
+  ./baz
+  ./baz/largefile
+  ./dirb
+  ./dirb/largefile
+  ./foo
+  $ cd ../../a
+
 #if hgweb
 Test display of largefiles in hgweb