Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H₀ , H ∈ C and if H₁ is similar to an isometric Hilbert module, then the sequence 0 → H₀ → H → H₁ → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that Extⁿ_C (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules similar to) unitary Hilbert modules are projective in the category H of all Hilbert modules. Connections with the conjecture that C is a proper subset of H are discussed.