diff --git a/tests/test_fread_small.py b/tests/test_fread_small.py
index <HASH>..<HASH> 100644
--- a/tests/test_fread_small.py
+++ b/tests/test_fread_small.py
@@ -54,3 +54,11 @@ def test_empty_strings(seed, repl):
     assert d1.topython() == src
 
 
+def test_select_some_columns():
+    # * Last field of last line contains separator
+    # * The file doesn't end with \n
+    # * Only subset of columns is requested
+    f = dt.fread(text='A,B,C\n1,2,"a,b"', columns={'A', 'B'})
+    assert f.internal.check()
+    assert f.names == ("A", "B")
+    assert f.topython() == [[1], [2]]
Add a test for fread (#<I>)