Wyo. Stat. § 1-21-516: Giving of further bond.

If within ten (10) days after levying the execution the judgment debtor enters into a further bond for stay of execution during the unexpired term of the first stay, and pays costs of the execution issued against him, the judge shall accept the further bond and recall the execution. The latest bond shall first be proceeded against until it appears by the return of the sheriff that there are no goods on which to levy, then proceedings shall be instituted on the first bond given.