Date calculation using GNU date

Using the GNU date command line utility, I know:

• how to substract 3 days from any given date:
  date -d "20110405 -3 days" "+%Y%m%d"
20110402

• how to get the last Friday from today:
  date -d "last friday" "+%Y%m%d"
20110408

But I don't know how to get the last Friday from any given date:
date -d "20110405 last friday" "+%Y%m%d"
Simply returns the given date:
20110405

Any ideas on how to do this? If a one-liner is not possible a few lines of script would also be helpful.