We report on an experimental study of the properties of a modular lead/scintillating-fiber calorimeter with a fully projective tower geometry. Although the calorimeter structure is monolythic, an effective segmentation into an electromagnetic and an hadronic section is achieved by separating the readout of the fibers running throughout the calorimeter from those starting beyond a depth of ∼ 25 radiation lengths. This feature is used for e/π separation. Discontinuities in the sampling fraction near the boundaries of the modules cause a signal nonuniformity for electrons, which can be corrected. Similar effects observed for high energy hadrons are discussed. Results are given on the energy and position resolution for electrons, on the signal linearity and on the absolute light yield. Pion showers were only partially contained in this detector. The information from a backing calorimeter, consisting of fast thin-gap wire chambers interleaved by iron slabs, significantly improves the energy resolution of the incompletely contained pion showers.