We analyze a small flare using imaging data at millimeter, microwave, and soft X-ray wavelengths and microwave and hard X-ray spectral observations. The remarkable aspect of this flare is evidence for the presence of MeV-energy electrons, which are responsible for the nonthermal millimeter emission, at a time when no hard X-rays from lower energy electrons are detected. This occurs during a smoothly varying phase, which is seen at radio wavelengths to last several minutes and is the brightest phase at millimeter wavelengths but is undetected in hard X-rays: it follows a brief spike of emission at flare onset, which has the more usual properties of impulsive events and features nonthermal microwave, millimeter, and hard X-ray emission. We interpretthe phase that is brightest at millimeter wavelengths as being due to efficient trapping of a relatively small number of nonthermal electrons, whereas during the hard X-ray emission, trapping is much less efficient, and the decay time is much shorter at all energies, which leads to a larger ratio of hard X-ray flux to radio flux. As in many previous events studied at millimeter wavelengths, there is a discrepancy between the electron energy spectral indices inferred from the milllimeter and hard X-ray data during the impulsive phase when both are detected: again it appears that the energy spectrum at 1 MeV must be significantly flatter than at several hundred keV and below. However, there are problems in reconciling quantitatively the energy spectra for the hard X-ray-emitting and radio-emitting components: based on the most plausible parameters, the radio-emitting electrons should produce most of the hard X-rays. One solution to this contradiction is to invoke a coronal magnetic field stronger than seems likely based on the photospheric magnetic field.