with larger data sizes and often unobservable variables, statistical models have become progressively larger and structurally complex and even computationally intractable. in applications, work-arounds have arisen that add say log-likelihoods and adjust for breakdown in bartlett relations, but usually with the loss of first order accuracy. meanwhile, likelihood asymptotics has sought progressively higher accuracy for p-value functions and now provides definitive third-order p-values and related likelihood functions. we apply the likelihood asymptotic approach to this combining problem and are able to convert composite likelihood to a fully first-order accurate procedure. the methods can then be extended to the combining of statistically dependent p-values and scores.