A modified Low procedure for constructing soft-photon amplitudes has been used to derive two general soft-photon amplitudes, a two-s -two-t special amplitude M"' " and a two-u -two-t special amplitude M"" ", where s, t, and u are the Mandelstam variables. M"' " depends only on the elastic T matrix evaluated at four sets of (s, t) fixed by the requirement that the amplitude be free of derivatives (BT/Bs and/or BT/Bt). Likewise M"""" depends only on the elastic T matrix evaluated at four sets of (u, t) also fixed by the requirement that the amplitude M"u "be free of derivatives (BT/Bu and/or AT/tjt). In -TsTts deriving these two amplitudes, we imposed the condition that M"' " and M " " reduce to M"and -Tu Tts~. . .
. -Ts TtsM", respectively, their tree-level approximations. The amplitude M"represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle s-channel exchange dia--Tu Tts grams, while the amplitude M"represents photon emission from a sum of one-particle t-channel exchange diagrams and one-particle u-channel exchange diagrams. The precise expressions for M "' " and