The verification of the absence of special nuclear material may be a key requirement in potential future warhead treaty verification. Total gamma-ray counting is a promising method for verifying the absence of nuclear material such as plutonium (Pu) or highly enriched uranium (HEU) while protecting any sensitive information that could be revealed by spectroscopic methods. Modeling and laboratory measurements have been performed on a variety of nuclear objects (NO) (items that contain Pu or HEU) and non-nuclear objects (NNO) (items that contain depleted uranium or low enriched uranium) to develop and test the technique and develop algorithms to confirm NNOs. The results from the two leading total gamma-ray count methods will be presented. The first method requires two total gamma-ray count measurements. One measurement is performed with a bare hand-held sodium iodide detector. The second measurement adds a thin lead attenuator. The attenuator gives the method some sensitivity to gamma-ray energy which is enough to separate many NOs from NNOs and verify absence in many cases. The second algorithm requires a single measurement but uses the total counts in multiple, carefully selected energy windows to separate NOs from NNOs. It leverages spectral shape but without requiring detailed analysis of the spectrum. Since a lack of counts can indicate absence of material or the presence of significant shielding, complementary off-axis transmission measurements through containers are being studied to set appropriate confidence limits on the results. Proof-of-concept measurements are planned for summer 2022. The latest project results will be presented. If successful, this project will provide a path toward development of a new tool for future warhead treaty verification. This work is supported by the US Dept. of Energy, National Nuclear Security Administration, Office of Defense Nuclear Nonproliferation Research and Development. This is PNNL document number PNNL-SA-169885.