Habeas/AEDPA.
Very complex. Here's our best guess on a first read:
When a state court re-evaluates a capital sentence due to a Federal Habeas writ, the case remains under collateral appeal, and is therefore not subject to non-retroactive changes in the substantive law.
In this case, the state court can consider a mitigating factor in a plenary consideration (whether Arizona's procedure here is genuinely de novo appears to be an open question) and impose the capital sentence without sending the case to a jury.
https://d3bsvxk93brmko.cloudfront.net/datastore/opinions/2015/12/30/12-16952.pdf
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.