Among the alignment models used in statistical machine translation (SMT), the hidden Markov model (HMM) is arguably the most elegant: it performs consistently better than IBM Model 3 and is very close in performance to the much more complex IBM Model 4. In this paper we discuss a model which combines the structure of the HMM and IBM Model 2. Using this surrogate, our experiments show that we can attain a similar level of alignment quality as the HMM model implemented in GIZA++ \cite{och03}. For this model, we derive its convex relaxation and show that it too has strong performance despite not having the local optima problems of non-convex objectives. In particular, the word alignment quality of this new convex model is significantly above that of the standard IBM Models 2 and 3, as well as the popular (and still non-convex) IBM Model 2 variant of \cite{dyer13}.