We address the problem of optical light pulses, called dressed pulses, which do not match the stationary pulse profile of a dispersion-managed (DM) fiber system and we theoretically analyze the associated radiation. Comparing hyperbolic-secant, raised-cosine, and Gaussian pulse envelopes, we show that the general radiation figure is highly sensitive to the input pulse profile. As common general features for these pulse profiles, we find a rich variety of dynamical states that includes weak-, moderate-, and strong-radiation states, depending on the map strength of the DM fiber system. We demonstrate the existence of two intervals of map strengths where the emitted radiation is of considerably low level. The first interval falls in a region of small map strengths where pulses are weakly dressed. In contrast, the second window of low radiation appears in the map strength region corresponding to strongly dressed pulses. As a major difference with respect to the pulse profile, we find that light pulses with Gaussian input profile produce less radiation in the fiber system than hyperbolic-secant or raised-cosine pulses can do. In particular, at the lower edge of the second window of low radiation, Gaussian light pulses with large initial dressing acquire the best ability to execute a stable nonradiative propagation over transoceanic distances.