The Perseverance rover is meant to collect samples of the martian surface for eventual return to Earth. The headspace gas present over the solid samples within the sample tubes will be of significant scientific interest for what it reveals about the interactions of the solid samples with the trapped atmosphere and for what it will reveal about the martian atmosphere itself. However, establishing the composition of the martian atmosphere will require other dedicated samples. The headspace gas as the sole atmospheric sample is problematic for many reasons. The quantity of gas present within the sample tube volume is insufficient for many investigations, and there will be exchange between solid samples, headspace gas, and tube walls. Importantly, the sample tube materials and preparation were not designed for optimal Mars atmospheric gas collection and storage as they were not sent to Mars in a degassed evacuated state and have been exposed to both Earth's and Mars' atmospheres. Additionally, there is a risk of unconstrained seal leakage in transit back to Earth, which would allow fractionation of the sample (leak-out) and contamination (leak-in). The science return can be improved significantly (and, in some cases, dramatically) by adding one or more of several strategies listed here in increasing order of effectiveness and difficulty of implementation: (1) Having Perseverance collect a gas sample in an empty sample tube, (2) Collecting gas in a newly-designed, valved, sample-tube-sized vessel that is flown on either the Sample Fetch Rover (SFR) or the Sample Retrieval Lander (SRL), (3) Adding a larger (50-100 cc) dedicated gas sampling volume to the Orbiting Sample container (OS), (4) Adding a larger (50-100 cc) dedicated gas sampling volume to the OS that can be filled with compressed martian atmosphere.