Recent studies have shown that non-uniform cellular automata (CA), where cellular rules need not necessarily be identical, can be co-evolved to perform computational tasks. This paper extends these studies by generalizing on a second aspect of CAs, namely their standard, homogeneous connectivity. We study non-standard architectures, where each cell has a small, identical number of connections, yet not necessarily from its most immediate neighboring cells. We show that such architectures are computationally more efficient than standard architectures in solving global tasks, and also provide the reasoning for this. It is shown that one can successfully evolve non-standard architectures through a two-level evolutionary process, in which the cellular rules evolve concomitantly with the cellular connections. Specifically, studying the global density task, we identify the average cellular distance as a prime architectural parameter determining cellular automata performance. We carry out a quantitative analysis of this relationship, our main results being: (1) performance is linearly dependent on the average cellular distance, with a high correlation coefficient; (2) high performance architectures can be co-evolved, concomitantly with the rules, and (3) low connectivity cost can be obtained as well as high performance. The evolutionary algorithm presented may have important applications to designing economical connectivity architectures for distributed computing systems.