G. Jank, E. Mues and L. Volkmann proved that if a nonconstant meromorphic functionfshares a nonzero finite valueaCM (counting multiplicities) with its first two derivativesf′and, thenf≡f′. It is also noted there that this is not the case fora=0. In this note we consider the casea=0 and IM (ignoring multiplicities) under certain andiiional conditions, one of which requires that the third order derivativeshould also share 0 IM withand the other is on the number of the zeros and multiple poles off. We prove that each of the conditions can reducef/f′to possibly a linear polynomial