Method of steepest descents; forming the contour?

Question

I am slightly confused about how, in the method of steepest descents, we go about forming the contour $c'$ from our original contour $c$. Clearly $c'$ must have the same end points as $c$ but I am confused about which of the other criterion it must satisfy:

1. Must go through a point where $h'(z)=0$ and through this point be following a path of steepest descent. or
   2. Made out of only paths of steepest descent and bridging paths where the integrand goes to zero. In this case we do not force it to go through a point where $h'(z)=0$.

Which of these is more standard, I have seen them both? (A source explaining both methods would be helpful).

[Assume we are dealing with the intergral: $$I(x)=\int_c f(t)e^{xh(t)}dt$$]