Modern network elements are increasingly required to deal with heterogeneous traffic. Recent works consider processing policies for buffers that hold packets with different processing requirement (number of processing cycles needed before a packet can be transmitted out) but uniform value, aiming to maximize the throughput, i.e., the number of transmitted packets. Other developments deal with packets of varying value but uniform processing requirement (each packet requires one processing cycle); the objective here is to maximize the total transmitted value. In this work, we consider a more general problem, combining packets with both nonuniform processing and nonuniform values in the same queue. We study the properties of various processing orders in this setting. We show that in the general case natural processing policies have poor performance guarantees, with linear lower bounds on their competitive ratio. Moreover, we show an adversarial lower bound that holds for every online policy. On the positive side, in the special case when only two different values are allowed, 1 and V, we present a policy that achieves competitive ratio 1 + (W+2)/V, where W is the maximal number of required processing cycles. We also consider copying costs during admission.