We present observations of the X-ray afterglow of GRB 050408 , a gamma-ray burst discovered by HETE-II . Swift began observing the field 42 min after the burst , performing follow-up over a period of 38 d ( thus spanning three decades in time ) . The X-ray light curve showed a steepening with time , similar to many other afterglows . However , the steepening was unusually smooth , over the duration of the XRT observation , with no clear break time . The early decay was too flat to be described in terms of standard models . We therefore explore alternative explanations , such as the presence of a structured afterglow or of long-lasting energy injection into the fireball from the central GRB engine . The lack of a sharp break puts constraints on these two models . In the former case , it may indicate that the angular energy profile of the jet was not a simple power law , while in the second model it implies that injection did not stop abruptly . The late decay may be due either to a standard afterglow ( that is , with no energy injection ) , or to a jetted outflow still being refreshed . A significant amount of absorption was present in the X-ray spectrum , corresponding to a rest-frame Hydrogen column density N _ { H } = 1.2 _ { -0.3 } ^ { +0.4 } \times 10 ^ { 22 } cm ^ { -2 } , indicative of a dense environment .