In this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions f composed with the Inner Product gadget g I P ( x y ) = i x i y i mod 2 of logarithmic size. In other words, given a function f : 0 1 n 0 1 with deterministic query complexity D ( f ) , we show that the deterministic communication complexity of the composed function f g n I P is ( D ( f ) log n ) , where f g n I P ( x y ) = f ( g I P ( x 1 y 1 ) g I P ( x n y n )) where x = ( x 1 x n ) , y = ( y 1 y n ) and each x i and y i are O ( log n ) bit strings. In [Raz, McKenzie FOCS 1997] and [Göös, et al. FOCS 2015], the simulation algorithm is implemented for functions composed with the Indexing gadget, where the size of the gadget is polynomial in the input length of the outer function f .