  We prove some necessary conditions for a link to be either concordant to a
quasi-positive link, quasi-positive, positive, or the closure of a positive
braid. The main applications of our results are a characterisation of positive
links with unlinking number $1$ and $2$, and a combinatorial criterion to test
if a positive link is the closure of a positive braid. Finally, we compile a
table of all positive and positive-braid prime links with less than $8$
crossings.
