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Smart phones, gaming consoles, and wireless routers are ubiquitous; the increasing diffusion of such devices with limited resources, together with society's unsatiated appetite for new applications, pushes companies to miniaturize their programs. Miniaturizing a program for a hand-held device is a time-consuming task often requiring complex decisions. Companies must accommodate conflicting constraints: customers' satisfaction with features may be in conflict with a device's limited storage, memory, or battery life. This paper proposes a process, MoMS, for the multi-objective miniaturization of software to help developers miniaturize programs while satisfying multiple conflicting constraints. It can be used to support the reverse engineering, next release problem, and porting of both software and product lines. The process directs the elicitation of customer pre-requirements, their mapping to program features, and the selection of the features to port. We present two case studies based on Pooka, an email client, and SIP Communicator, an instant messenger, to demonstrate that MoMS supports optimized miniaturization and helps reduce effort by 77%, on average, over a manual approach.