The present invention relates to a drug delivery device (100) comprising :- a reservoir (10) for containing a medical product,- a distally projecting end-piece (20) having an outer surface and a total length LT measured along a longitudinal axis A of said end-piece, said end-piece defining an axial passageway for the transfer of said medical product contained in said reservoir,wherein a gripping surface (23) is provided on a portion (22) of said outer surface, said portion being located in a distal region (21a) of said end-piece, the length LC of said portion (22) representing at most 40%, preferably less than 33%, of the total length LT of the end-piece.The invention further relates to an assembly comprising such a drug delivery device and an adaptor intended to be mounted onto the end-piece.