Dynamic histogram shifting (DHS) is a generation of the conventional histogram shifting (HS) technique for reversible image watermarking. Its superior embedding performance is achieved at the cost of significantly increased computational burden incurred by estimating the capacity parameters via multi-rounds of embedding iterations. In this work, we propose an analytical framework on estimating the optimal capacity parameters for DHS-based reversible image watermarking. We demonstrate that such parameter estimation can be cast as a convex optimization problem, which can be numerically solved in an efficient manner. The estimated values can then be utilized to facilitate a local search algorithm to obtain the truly optimal ones with much lowered complexity. Experimental results are provided to verify the validity of our findings.