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This chapter first consolidates a set of important heuristic strategies used for constructing innovative scientific models from three books, including studies in the history of genetics and electromagnetism, and an expert think-aloud study in mechanics. Twenty-four strategies are identified, most of which are field-general. Patterns in their use suggest a partially organized hierarchy of interconnected strategies and substrategies, contrary to the view that heuristics are simply tried in random order. Strategies at four different size and time scale levels are described, including larger Modeling Cycle Phases of model generation, evaluation, and modification, each of which can utilize many smaller Tactical Heuristics as substrategies, e.g., analogy, or testing predictions from the model. These in turn can utilize Grounded Imagistic Processes, such as imagistic mental simulation, an important alternative to deduction for evaluating a model by running it. The framework links higher level, serially organized processes with lower level, imagery-based processes. Its intermediate degree of organization is neither anarchistic, nor fully algorithmic. Possible benefits of organization are narrowing the search space involved and balancing sources of model construction and criticism for productive creativity. Unorganized, spontaneous processes are also discussed, along with their possible benefits.