We study overnight interbank interest rates paid by banks in Norway over the period 2006-2009. We observe large variations in interest rates across banks and over time. During the financial crisis, the interest rates are found to be substantially below indicative quotes of interest rates provided by major banks. Our econometric model attributes the interest rate variation partly to differences in banks' characteristics including relative size and connectedness, implying favorable terms for banks of systemic importance. Moreover, interest rates are found to depend not only on overall liquidity in the interbank market, but possibly on its distribution among banks as well, suggesting exploitation of market power by banks with surplus liquidity. There is also evidence of stronger effects on interest rates of systemic importance, credit ratings and liquidity demand and supply since the start of the current financial crisis.