  We present the simplest criterion that determines the direction of the Hopf
bifurcations of the delay differential equation $x'(t)=-\mu f(x(t-1))$, as the
parameter $\mu$ passes through the critical values $\mu_k$. We give a complete
classification of the possible bifurcation sequences. Using this information
and the Cooke-transformation, we obtain local estimates and monotonicity
properties of the periods of the bifurcating limit cycles along the
Hopf-branches. Further, we show how our results relate to the often required
property that the nonlinearity has negative Schwarzian derivative.
