Economists consider the banking system the heart of a country’s economy because it pumps the money through the economy thus driving production, exchange and its growth. Competition in banking industry has become acute since the late 1980s liberalisation of the sector; it was intensified after 2005 consolidation, the keenest aspect of the competition is the competition for deposits. Nigerian banks have deployed an array of tools to position themselves for this battle for deposits, ranging from glitzy branding and marketing campaigns to the deployment of smart marketing staff. These banks also attract customers with the deployment of e-banking solutions and the construction of an ever-increasing number of branches. This work set out to find out the factors that affect the decision by individuals to open bank accounts in a particular bank, with a view to using statistical tools to evaluate the relative importance of each factor that attracts customers to a particular bank, determine the strongest factor, and also depict some types of products/services banks should include in their array. The main analysis was done with the use (aid) of SPSS’s version of full profile conjoint analysis, where the utilities of the profile cards were analysed. However it was deduced that security of funds was the most considered factor, followed by customer relations, but the least considered was interest rates. A small descriptive analysis was done, and the result confirms what we deduced from conjoint analysis. Banks are advised to include savings plus into their array, employ smart staff and train them to be efficient and friendly, provide Automated Teller Machine ATM in strategic locations, and ensure branding right product for the right set of people or organisations.