Summary: We apply the recently proposed integrability criterion for differential- difference systems (that blends the classical Painlevé analysis with singularity confinement for discrete systems) to a class of first-order differential-delay equations. Our analysis singles out the family of bi- Riccati equations, as integrability candidates. Among these equations that pass the test some are integrable in a straightforward way (usually by reduction to a standard Riccati equation for some transformed variable) while the remaining ones define new hysterodifferential forms of the Painlevé transcendental equations.