A study of runaway electrons has been made during the current rise stage of discharges in tokamak LT-4. The bremsstrahlung from a small target just inside the plasma boundary was measured as a function of q (target). The correlation between X-ray bursts and integer q was established over a large range of q-values. It is suggested that lower-energy runaway electrons are carried with the expanding integer-q regions and that an upper limit could be placed on the energy of electrons surviving within the plasma.