Finding a list of heritable traits using GCTA

Question

[samuelandjw]

Suppose I have a list of traits, and I want to know which traits are heritable (not sure if this is a well-defined question ...) using GCTA GREML. For heritable traits, I want to know the exact magnitude of the heritability. Now, should I

1. Test for $h_g^2$=0 using unconstrained ($h_g^2$ could be negative) GREML for each trait.
2. For each significant trait (not sure if multiple testing is appropriate here), re-run constrained GREML to obtain the estimate of $h_g^2$.

Or

1. Run constrained GREML and declare traits with significant p values or $h_g^2$ larger than a preset threshold as "heritable".

Which method is correct?