diff --git a/Lib/fontTools/cffLib/__init__.py b/Lib/fontTools/cffLib/__init__.py
index 4ad0e4420..cd239053c 100644
--- a/Lib/fontTools/cffLib/__init__.py
+++ b/Lib/fontTools/cffLib/__init__.py
@@ -2242,6 +2242,12 @@ class BaseDict(object):
 		return self.compilerClass(self, strings, parent, isCFF2=isCFF2)
 
 	def __getattr__(self, name):
+		if name[:2] == name[-2:] == "__":
+			# to make deepcopy() and pickle.load() work, we need to signal with
+			# AttributeError that dunder methods like '__deepcopy__' or '__getstate__'
+			# aren't implemented. For more details, see:
+			# https://github.com/fonttools/fonttools/pull/1488
+			raise AttributeError(name)
 		value = self.rawDict.get(name, None)
 		if value is None:
 			value = self.defaults.get(name)