Timed automata is a fundamental modeling formalism for real-time systems. During the design of such real-time systems, often the system information is incomplete, and design choices can vary. These uncertainties can be integrated to the model via parameters and labelled transitions. Then, the design can be completed by tuning the parameters and restricting the transitions via controller synthesis. These problems, namely parameter synthesis and controller synthesis, are studied separately in the literature. Herein, these are combined to generate an automaton satisfying the given specification by both parameter tuning and controller synthesis, thus exploring all design choices. First, it is shown that the negative decidability results derived for the parameter synthesis problem apply to the proposed problem. Then, a specific version of the problem is studied, where the specification is to reach a target set and parameters can take values from bounded integer sets. An algorithm based on depth first analysis combined with an iterative feasibility check is presented to solve the proposed problem. The correctness and the completeness (under mild assumptions) of the developed algorithm are proven. The findings of the paper are illustrated on an example drawn from scheduling.