The original Thom conjecture states that holomorphic curves are minimal genus representatives of 2-dimensional homology classes in CP^2. It has been known for a long time that the analogous claim for codimension 2 homology classes in CP^n does not hold; Freedman showed that for n even any such class is represented by a submanifold which has smaller middle homology than a complex hypersurface representing this class and which on the level of homotopy behaves as a complex hypersurface. We consider the case of 4-manifolds in CP^3 and show that the rank of the 2nd homology in any given class can be significantly reduced. This is joint work with D. Ruberman and M. Slapar.