Optical-fiber sensors that use fluorescent probes located in the fiber cladding are of great interest for monitoring physical and chemical properties in their environment. The interrogation of a fluorophore with a short laser pulse propagating through the fiber core allows for the measurement of the location of the fluorophore by measuring the time delay between the exciting pulse and the returning fluorescence pulse. The spatial resolution of such an array of fluorescent sensors is limited since a minimum separation of the fluorophores is required to resolve returning light pulses. For many applications a closer spacing of sensor regions is desirable, particularly for fibers prepared by using our recently introduced one-dimensional combinatorial chemistry method [A. W. Schwabacher et al., J. Am. Chem. Soc. 121, 8669 (1999)]. This method allows for efficient preparation of large, diverse, and densely packed linear arrays of sensors. We demonstrate that by using a second fiber as an optical delay line, the minimum spacing between adjacent sensor regions can be well below the fluorescence lifetime limit. Since the coupling between the two fibers is evanescent, the attenuation of the excitation pulse is low, making long arrays of sensor regions feasible. Moreover, we identify the conditions that allow for the optical readout of long arrays of sensors.