In response to the perceived problems with the "pure" waterfall model, many modified waterfall models have been introduced. These models may address some or all of the criticisms of the "pure" waterfall model.
These include the Rapid Development models that Steve McConnell calls "modified waterfalls" (see especially p. 143-147): Peter DeGrace's "sashimi model" (waterfall with overlapping phases), waterfall with subprojects, and waterfall with risk reduction. Other software development model combinations such as "incremental waterfall model" also exist
Royce's final model
Winston W. Royce's final model, his intended improvement upon his initial "waterfall model", illustrated that feedback could (should, and often would) lead from code testing to design (as testing of code uncovered flaws in the design) and from design back to requirements specification (as design problems may necessitate the removal of conflicting or otherwise unsatisfiable / undesignable requirements). In the same paper Royce also advocated large quantities of documentation, doing the job "twice if possible" (a sentiment similar to that of Fred Brooks, famous for writing the Mythical Man Month, an influential book in software project management, who advocated planning to "throw one away"), and involving the customer as much as possible (a sentiment similar to that of Extreme Programming).