We study field-monitoring applications in which sensors are deployed in large numbers and the sensing process is expensive. In such applications, nodes should use the minimum possible sensing ranges to prolong the “coverage time” of the network. We investigate how to determine such minimum ranges in a distributed fashion when the nodes are location-unaware. We develop a distributed protocol (SRAP) that assigns shorter ranges to nodes with less remaining batteries. To handle location-unawareness, we develop a novel algorithm (VICON) for determining the virtual coordinates of the neighbors of each sensor. VICON relies on approximate neighbor distances and 2-hop neighborhood information. Our simulations indicate that SRAP results in significant coverage time improvement even under inaccurate distance estimation.