The 4:10 dme flight is the overnighter on the 767 and the 3:55 is the day flight, so being fair to the OP if he flies off at 9:30 ish and arrives 4 :10 later and goes straight to work after losing the night, CW is needed on this run, p,us it saves a work day for the company.

When i was doing work DME-LHR-DME and policy was 7 hours or more to get business, i always got agreement to go business as otherwise it took three days and two hotel rooms and the company were more interested in getting three days work out of me than saving a few quid