diff --git a/msgpack/_unpacker.pyx b/msgpack/_unpacker.pyx
index 3c81808f..b0e84528 100644
--- a/msgpack/_unpacker.pyx
+++ b/msgpack/_unpacker.pyx
@@ -325,6 +325,8 @@ cdef class Unpacker:
     cdef object unicode_errors
     cdef Py_ssize_t max_buffer_size
     cdef uint64_t stream_offset
+    # stream_offset at the start of an incomplete object
+    cdef uint64_t object_offset
     cdef bint _unpacking
 
     def __dealloc__(self):
@@ -486,6 +488,8 @@ cdef class Unpacker:
             raise RuntimeError("Unpacker cannot be called recursively while unpacking is in progress")
         if self.ctx.execute != NULL and self.ctx.execute != execute:
             raise ValueError("Cannot switch unpacking methods while an object is incomplete")
+        if self.ctx.execute == NULL:
+            self.object_offset = self.stream_offset
 
         self._unpacking = True
         try:
@@ -585,6 +589,9 @@ cdef class Unpacker:
         number of bytes that were read from the input, also the starting
         position of the next object.
         """
+        if self.ctx.execute != NULL:
+            # Part of the next object has been decoded, but it still starts here.
+            return self.object_offset
         return self.stream_offset
 
     def __iter__(self):
diff --git a/test/test_sequnpack.py b/test/test_sequnpack.py
index 904be42f..15682721 100644
--- a/test/test_sequnpack.py
+++ b/test/test_sequnpack.py
@@ -169,3 +169,22 @@ def test_unpack_tell():
         m2 = next(unpacker)
         assert m == m2
         assert o == unpacker.tell()
+
+
+def test_unpack_tell_incomplete_object():
+    # tell() is where the next object starts, even when only part of it has arrived.
+    first = packb([1, 2, 3])
+    second = packb(["x" * 40, "y" * 40])
+    packed = first + second
+    for cut in (len(first) + 1, len(first) + 3, len(first) + 45):
+        unpacker = Unpacker()
+        unpacker.feed(packed[:cut])
+        assert list(unpacker) == [[1, 2, 3]]
+        assert unpacker.tell() == len(first)
+        unpacker.feed(packed[cut:])
+        assert list(unpacker) == [["x" * 40, "y" * 40]]
+        assert unpacker.tell() == len(packed)
+
+        unpacker = Unpacker(io.BytesIO(packed[:cut]), read_size=16)
+        assert list(unpacker) == [[1, 2, 3]]
+        assert unpacker.tell() == len(first)