Designing efficient processor allocation algorithms is one of the major issues to build large high performance Chip Multiprocessors (CMPs). The task of the processor allocator (PA) is to assign one or more processors for an incoming job. In this paper, we propose two new contiguous processor allocation algorithms, Better First Fit (BFF) and Improved Better First Fit (IBFF), for CMPs based on 2-D mesh networks. Our proposed algorithms outperform other existing allocation strategies based on busy array approach such as First Fit (FF) and Improved First Fit (IFF) using a faster scanning of the bit-map matrix. Evaluation of BFF and IBFF were done with different sets of jobs over different network sizes and job dispatching approaches. According to the job size, BFF is faster than IFF by up to 63.1% or 18.5% in average for all job sizes evaluated. IBFF, when set with best parameters, is 54.8% faster than IFF and 4% faster than BFF for a random mix of job sizes.