Galactic cosmic ray (GCR) secondary/primary ratios such as B/C and (Sc+Ti+V)/Fe are commonly used to determine the mean amount of interstellar material through which cosmic rays travel before escaping from the Galaxy (Λ esc ). These ratios are observed to be energy-dependent, with a relative maximum at ∼1 GeV/nucleon, implying a corresponding peak in Λ esc . The decrease in Λ esc at energies above 1 GeV/nucleon is commonly taken to indicate that higher energy cosmic rays escape more easily from the Galaxy. The decrease in Λ esc at energies <1 GeV/nuc is more controversial; suggested possibilities include the effects of a galactic wind or the effects of distributed acceleration of cosmic rays as they pass through the interstellar medium. We consider two possible explanations for the low energy decrease in Λ esc and attempt to fit the combined, high-resolution measurements of secondary/primary ratios from ∼0.1 to 35 GeV/nuc made with the CRIS instrument on ACE and the C2 experiment on HEAO-3. The first possibility, which hypothesizes an additional, local component of low-energy cosmic rays that has passed through very little material, is found to have difficulty simultaneously accounting for the abundance of both B and the Fe-secondaries. The second possibility, suggested by Soutoul and Ptuskin, involves a new form for Λ esc motivated by their diffusion-convection model of cosmic rays in the Galaxy. Their suggested form for Λ esc (E) is found to provide an excellent fit to the combined ACE and HEAO data sets.