A coffee maker (10) has at least one removable portafilter (11) that can be inserted into a holder (12) on the coffee machine to carry out brewing. The coffee maker has a hot water maker (28) for producing and dispensing hot water under pressure and at least one coffee mill (19). A filter element (33) is provided for repeated pressure-tight closing and opening of the portafilter (11) inserted into the holder (12) and a chute (23) is provided for introducing coffee powder (16) from the coffee mill (19) into the open portafilter (11) that has been inserted into the holder (12).