Embodiments of medical infusion pumps are provided that include structural elements for providing sources of compliance within a fluid path within the pump. Some preferred embodiments provide implantable infusion pumps with compliance positioned between an exit port of a pumping mechanism and an outlet (e.g. an opening in a catheter) of the infusion pump. Other embodiments provide compliance in fluid path in proximity to entrance port of the pumping mechanism. Insertion of compliance in a flow path that is down stream of the pumping mechanism may aid in minimizing negative effects associated with attempting to force fluid through a restricted flow path that is further down-stream, such as that offered by a catheter or other outlet component. Insertion of compliance before the pumping mechanism may aid in reducing negative effects associated with an up stream restricted flow path, such as that which might be offered by a rigid filter located between the reservoir and the pumping mechanism. Several structural components, assemblies, or configurations may be used as sources of compliance. For example, compressible structures (e.g. pillows, drums) are used within a side port of the infusion pump. The compressible structures may quickly distort to accommodate for a large impulse of fluid into the flow path that can not otherwise be readily dealt with. The compression, in turn, results in a restoring force being exerted that returns the structure substantially to its original volume so as to slowly force fluid from the flow path.