A connector apparatus for small-bore medical tubing includes a male connector (20) with a dome (22) which fits into a mating cavity (42) of a female connector (40) when the two connectors are coupled together. A fluid channel extends through the connectors, the dome, and into the cavity to form a continuous fluid passageway when the connectors are coupled together. The dome is compressed into the cavity to form a fluid-tight connection when the connectors are coupled together. Each connector has a coupling structure which mates with the other to compress the connectors together when fully engaged. The connectors are engaged by inserting the dome of one of the connectors into the cavity of the other connector, then rotating the connectors to fully couple them together.