Several algorithmic models have been proposed to estimate software costs and other management parameters. Early prediction of completion time is absolutely essential for proper advance planning and aversion of the possible ruin of a project. L.H. Putnam's (1978) SLIM (Software LIfecycle Management) model offers a fairly reliable method that is used extensively to predict project completion times and manpower requirements as the project evolves. However, the nature of the Norden/Rayleigh curve used by Putnam renders it unreliable during the initial phases of the project, especially in projects involving a fast manpower buildup, as is the case with most software projects. In this paper, we propose the use of a model that improves early prediction considerably over the Putnam model. An analytic proof of the model's improved performance is also demonstrated on simulated data.