Delete Budget Code with Activity

We have revamped our naming convention for "budgets".  I want to delete the old budget codes.  I went into General Ledger, Setup, GL Options, "Budget" tab.  When I click on the old budget name I want to delete, I get a message that states I cannot delete a budget with activity in it.  I tried to zero out all budgeted numbers and then tried to delete, but I get the same message.

Is there a way to delete the old budget and then delete the budget code?

Thanks!