A syringe adaptor includes a body, shaped to define a body lumen, a syringe fitting at a proximal end of the body, configured to connect to a distal end of a syringe, a needle extending distally from the syringe fitting into the body lumen, a septum housing, and an elastomeric septum mounted inside the septum housing. The septum includes a proximal face, shaped to define an aperture having an aperture diameter, and a distal face. The septum is shaped to define a cavity, joined to the aperture, having a cavity diameter that is larger than the aperture diameter. The septum housing is configured to slide proximally within the body lumen such that a distal end of the needle contained in the cavity passes through the distal face of the septum. Other embodiments are also described.