The inverse β-decay of ¹¹⁵In provides a low-threshold direct-counting neutrino detector. Unfortunately, the radioactive background due to ¹¹⁵In β-decay may be a very grave obstacle in the development of a detector for pp solar neutrinos. We suggest that this background can be efficiently suppressed in searches for higher energy solar neutrinos, e.g. from Be, p-e-p and ⁸B. A signal/background ratio of 10-30 is expected. It may be possible to have a count rate of 0.2 events/d with a detector consisting of 10 tons of indium and about 15 m³ of liquid xenon. Unfortunately, pp neutrinos cannot be detected in this set-up.