Efficient Software Development Methodology (ESDM) provides an efficient way to develop software. It seeks to maximize the contributions of the top developers since according to various studies 80% of the work is done by only 20% of the developers on the average project. The difference between the best and worst developer on a project is somewhere between 10 to 1, and 28 to 1 depending on the study. See Facts and Fallacies of Software Engineering by Robert L. Glass Fact 2 for more information about this.
ESDM is not a methodology that falls under the agile methodology category. Most if not all agile methods use short iterations and incremental deliveries. This is wasteful because of the overhead involved. Agile practices like short iterations, pair programming, shared code ownership, test first, incremental integration practices, etc. are a poor and inefficient way to run a software project.
ESDM follows a set of structured and logical practices with significant emphasis on testing. Developers always know where they are going and what to do next. Requirements are analyzed first, followed by determining the software specifications, design through pseudocode, followed by coding, and then extensive testing which consists of debugging the code line by line, unit tests, and interface tests.