A needleless luer access connector is disclosed having a septum disposed in a housing. The septum has a proximal portion with a cross section, a medial portion with a cross section smaller than the cross section of the proximal portion, and a distal portion. A longitudinal slit extends through the septum from the proximal portion to the distal portion. The septum and housing are designed so that septum will not be rotated or removed from the housing when the connector is accessed by a male luer taper. In addition, the septum and housing are designed to bias the slit at the distal portion closed and so a male luer connector does not have to extend completely through the distal portion to open the slit at the distal portion. Finally, the septum and housing are designed to minimize the amount of dead space in the connector when accessed with a male luer taper.