There is growing concern over the frequent cases of cost overruns, and underestimation in software cost, especially, indigenous software products. This has a lot to do with the choice of Cost-estimation tools, techniques and models deployed. Constructive Cost Model (COCOMO) II model has been adjudged as the most reliable and accurate. However, the existing cost drivers/variables of this model (COCOMO II) do not capture fully the uniqueness of Nigeria's computing environment. This paper has highlighted the strengths and weaknesses of COCOMO II considering the hierarchy of COCOMO. A new algorithm was proposed to effectively enhance the cost estimation effort of indigenous software in Nigeria Njoku A. Obilor et al.