diff --git a/dill/_dill.py b/dill/_dill.py
index 668534db..146ab9b6 100644
--- a/dill/_dill.py
+++ b/dill/_dill.py
@@ -367,7 +367,7 @@ def __init__(self, file, *args, **kwds):
         self._refonfail = False #settings['dump_module']['refonfail'] if _refonfail is None else _refonfail
         self._strictio = False #_strictio
         self._postproc = OrderedDict()
-        self._file = file  # for the logger
+        self._file_tell = getattr(file, 'tell', None)  # for logger and refonfail
 
     def dump(self, obj): #NOTE: if settings change, need to update attributes
         # register if the object is a numpy ufunc
@@ -421,32 +421,29 @@ def save(self, obj, save_persistent_id=True, *, name=None):
         if not self._refonfail:
             super().save(obj, save_persistent_id)
             return
-        if self.framer.current_frame:
-            # protocol >= 4
-            self.framer.commit_frame()
-            stream = self.framer.current_frame
-        else:
-            stream = self._file
-        position = stream.tell()
+        # Disable framing (right after the framer.init_framing() call at dump()).
+        self.framer.current_frame = None
+        # Store initial state.
+        position = self._file_tell()
         memo_size = len(self.memo)
         try:
             super().save(obj, save_persistent_id)
         except UNPICKLEABLE_ERRORS + (AttributeError,) as error_stack:
-            # AttributeError may happen in save_global() call for child object.
+            # AttributeError may happen in the save_global() call from a child object.
             if (type(error_stack) == AttributeError
                     and "no attribute '__name__'" not in error_stack.args[0]):
                 raise
-            # roll back the stream
-            stream.seek(position)
-            stream.truncate()
-            # roll back memo
+            # Roll back the stream.
+            self._file_seek(position)
+            self._file_truncate()
+            # Roll back memo.
             for _ in range(len(self.memo) - memo_size):
-                self.memo.popitem()  # LIFO order is guaranteed for since 3.7
+                self.memo.popitem()  # LIFO order is guaranteed since 3.7
             try:
                 self.save_global(obj, name)
             except (AttributeError, PicklingError) as error:
                 if getattr(self, '_trace_stack', None) and id(obj) == self._trace_stack[-1]:
-                    # roll back trace state
+                    # Roll back trace state.
                     self._trace_stack.pop()
                     self._size_stack.pop()
                 raise error from error_stack
diff --git a/dill/logger.py b/dill/logger.py
index 7b6afcdd..385c862d 100644
--- a/dill/logger.py
+++ b/dill/logger.py
@@ -148,7 +148,7 @@ def trace(self, pickler, msg, *args, obj=None, **kwargs):
         size = None
         try:
             # Streams are not required to be tellable.
-            size = pickler._file.tell()
+            size = pickler._file_tell()
             frame = pickler.framer.current_frame
             try:
                 size += frame.tell()
diff --git a/dill/session.py b/dill/session.py
index 9e545f1c..3da31318 100644
--- a/dill/session.py
+++ b/dill/session.py
@@ -203,10 +203,12 @@ def dump_module(
             similar but independent from ``dill.settings[`byref`]``, as
             ``refimported`` refers to virtually all imported objects, while
             ``byref`` only affects select objects.
-        refonfail: if `True`, objects that fail to be saved by value will try to
-            be saved by reference.  If it also fails, saving their parent
+        refonfail: if `True`, objects that fail to pickle by value will try to
+            be saved by reference.  If this also fails, saving their parent
             objects by reference will be attempted recursively.  In the worst
-            case scenario, the module itself may be saved by reference.
+            case scenario, the module itself may be saved by reference.  Note:
+            The file-like object must be seekable and truncable with this
+            option set.
         **kwds: extra keyword arguments passed to :py:class:`Pickler()`.
 
     Raises:
@@ -302,9 +304,17 @@ def dump_module(
         pickler._main = main     #FIXME: dill.settings are disabled
         pickler._byref = False   # disable pickling by name reference
         pickler._recurse = False # disable pickling recursion for globals
-        pickler._refonfail = refonfail
         pickler._session = True  # is best indicator of when pickling a session
         pickler._first_pass = True
+        if refonfail:
+            pickler._refonfail = True  # False by default
+            pickler._file_seek = getattr(file, 'seek', None)
+            pickler._file_truncate = getattr(file, 'truncate', None)
+            if hasattr(file, 'seekable') and not file.seekable():
+                pickler._file_seek = None
+            if pickler._file_seek is None or pickler._file_truncate is None:
+                raise TypeError("file must have 'tell', 'seek' and 'truncate'"
+                                " attributes if the 'refonfail' option is set.")
         pickler.dump(main)
     return