A tape drive-implemented method, according to one embodiment, includes: detecting a read error, and sending one or more instructions to perform a first re-read attempt on a portion of a magnetic tape corresponding to the read error. In response to determining that the first re-read attempt was unsuccessful, a range of tension settings is selected. A range of lateral offsets is also selected. Moreover, one or more instructions are sent to apply each unique combination of a tension setting from the range of tension settings and a lateral offset from the range of lateral offsets. For each of the unique combinations applied, one or more instructions are sent to perform a second phase re-read attempt on the portion of the magnetic tape corresponding to the read error. Furthermore, a determination is made as to whether the second phase re-read attempt was performed successfully for any of the unique combinations.