— Consider the problem of resource allocation on the downlink of a cellular OFDMA system. A fairness constraint is defined by a minimum data rate, a maximum bit-error rate and a maximum outage probability. This paper proposes a lowcomplexity resource allocation algorithm that requires a reduced feedback-overhead. Under a partial Channel-State Information, we derive the optimal subcarrier and power allocation that provides the best overall outage performance using the lowest possible number of subcarriers. Unneeded subcarriers lend themselves to interference-free use in other cells assuming some inter-cell coordination. We first evaluate the maximum achievable number of users when all subcarriers are used. This defines an upper-bound on system load. Then, for an arbitrary load ratio, we describe the corresponding resource allocation and provide an analytic upper-bound on the achievable outage probability.