diff --git a/newsfragments/3714.minor b/newsfragments/3714.minor
new file mode 100644
index 000000000..e69de29bb
diff --git a/src/allmydata/scripts/tahoe_cp.py b/src/allmydata/scripts/tahoe_cp.py
index fb86ff0ec..df4965dc7 100644
--- a/src/allmydata/scripts/tahoe_cp.py
+++ b/src/allmydata/scripts/tahoe_cp.py
@@ -701,6 +701,8 @@ class Copier(object):
 
 
     def need_to_copy_bytes(self, source, target):
+        # This should likley be a method call! but enabling that triggers
+        # additional bugs. https://tahoe-lafs.org/trac/tahoe-lafs/ticket/3719
         if source.need_to_copy_bytes:
             # mutable tahoe files, and local files
             return True
diff --git a/src/allmydata/test/cli/test_cp.py b/src/allmydata/test/cli/test_cp.py
index d198a832c..d55bc01bd 100644
--- a/src/allmydata/test/cli/test_cp.py
+++ b/src/allmydata/test/cli/test_cp.py
@@ -238,6 +238,66 @@ class Cp(GridTestMixin, CLITestMixin, unittest.TestCase):
 
         return d
 
+    @defer.inlineCallbacks
+    def test_cp_duplicate_directories(self):
+        self.basedir = "cli/Cp/cp_duplicate_directories"
+        self.set_up_grid(oneshare=True)
+
+        filename = os.path.join(self.basedir, "file")
+        data = b"abc\xff\x00\xee"
+        with open(filename, "wb") as f:
+            f.write(data)
+
+        yield self.do_cli("create-alias", "tahoe")
+        (rc, out, err) = yield self.do_cli("mkdir", "tahoe:test1")
+        self.assertEqual(rc, 0, (rc, err))
+        dircap = out.strip()
+
+        (rc, out, err) = yield self.do_cli("cp", filename, "tahoe:test1/file")
+        self.assertEqual(rc, 0, (rc, err))
+
+        # Now duplicate dirnode, testing duplicates on destination side:
+        (rc, out, err) = yield self.do_cli(
+            "cp", "--recursive", dircap, "tahoe:test2/")
+        self.assertEqual(rc, 0, (rc, err))
+        (rc, out, err) = yield self.do_cli(
+            "cp", "--recursive", dircap, "tahoe:test3/")
+        self.assertEqual(rc, 0, (rc, err))
+
+        # Now copy to local directory, testing duplicates on origin side:
+        yield self.do_cli("cp", "--recursive", "tahoe:", self.basedir)
+
+        for i in range(1, 4):
+            with open(os.path.join(self.basedir, "test%d" % (i,), "file"), "rb") as f:
+                self.assertEquals(f.read(), data)
+
+    @defer.inlineCallbacks
+    def test_cp_immutable_file(self):
+        self.basedir = "cli/Cp/cp_immutable_file"
+        self.set_up_grid(oneshare=True)
+
+        filename = os.path.join(self.basedir, "source_file")
+        data = b"abc\xff\x00\xee"
+        with open(filename, "wb") as f:
+            f.write(data)
+
+        # Create immutable file:
+        yield self.do_cli("create-alias", "tahoe")
+        (rc, out, _) = yield self.do_cli("put", filename, "tahoe:file1")
+        filecap = out.strip()
+        self.assertEqual(rc, 0)
+
+        # Copy it:
+        (rc, _, _) = yield self.do_cli("cp", "tahoe:file1", "tahoe:file2")
+        self.assertEqual(rc, 0)
+
+        # Make sure resulting file is the same:
+        (rc, _, _) = yield self.do_cli("cp", "--recursive", "--caps-only",
+                                       "tahoe:", self.basedir)
+        self.assertEqual(rc, 0)
+        with open(os.path.join(self.basedir, "file2")) as f:
+            self.assertEqual(f.read().strip(), filecap)
+
     def test_cp_replaces_mutable_file_contents(self):
         self.basedir = "cli/Cp/cp_replaces_mutable_file_contents"
         self.set_up_grid(oneshare=True)
diff --git a/src/allmydata/test/cli/test_put.py b/src/allmydata/test/cli/test_put.py
index c6a577074..03306ab71 100644
--- a/src/allmydata/test/cli/test_put.py
+++ b/src/allmydata/test/cli/test_put.py
@@ -486,3 +486,20 @@ class Put(GridTestMixin, CLITestMixin, unittest.TestCase):
                       self.failUnlessReallyEqual(rc_out_err[1], DATA))
 
         return d
+
+    def test_no_leading_slash(self):
+        self.basedir = "cli/Put/leading_slash"
+        self.set_up_grid(oneshare=True)
+
+        fn1 = os.path.join(self.basedir, "DATA1")
+
+        d = self.do_cli("create-alias", "tahoe")
+        d.addCallback(lambda res:
+                      self.do_cli("put", fn1, "tahoe:/uploaded.txt"))
+        def _check(args):
+            (rc, out, err) = args
+            self.assertEqual(rc, 1)
+            self.failUnlessIn("must not start with a slash", err)
+            self.assertEqual(len(out), 0, out)
+        d.addCallback(_check)
+        return d