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Assessment of the effects of crop management practices on soil physical properties is largely limited to soil moisture content, air content or bulk density, which can take considerable time to change. However, soil pore space indices evolve rapidly and could quickly detect changes in soil properties resulting from crop management practices, but they are not often measured. The objective of this study was to investigate how soil pore space indices—relative gas diffusion coefficient (Ds/Do) and pore tortuosity factor (τ)—are affected by tillage system (TL), cover crop (CC) and crop rotation (CR). A study was conducted on silt loam soil at Freeman farm, Lincoln University of Missouri during the 2011 to 2013 growing seasons. The experiment design was a randomized complete block with two tillage systems (no tillage or no-till vs conventional tillage), two cover crops (no rye vs cereal rye (Secale cereale L.)) and four crop rotations (continuous corn (Zea mays L.), continuous soybean (Glycine max L.), corn–soybean and soybean–corn successions). All the treatments were replicated three times for a total of 48 experimental units. Soils were collected from two sampling depths (SD), 0–10 and 10–20 cm, in each treatment and soil physical properties, including bulk density (BD), air-filled porosity (AFP, fa) and total pore space (TPS, Φ), were calculated. Gas diffusivity models following AFP and/or TPS were used to predict Ds/Do and τ values. Results showed that, overall, Ds/Do was significantly increased in no-tilled plots planted to cereal rye in 2012 (p = 0.001) and in 2013 (p = 0.05). No-tilled continuous corn, followed by continuous soybean and no-tilled soybean–corn rotations had the highest Ds/Do values, respectively. In magnitude, Ds/Do was also increased in no-till plots at the lower depth (10–20 cm). No-tilled plots planted with cereal rye significantly reduced τ in 2012 (p = 0.001) and in 2013 (p = 0.05). Finally, at the upper depth (0–10 cm), the no-tilled corn–soybean rotation and the tilled soybean–corn rotation had the lowest τ. However, at the lower depth (10–20 cm), the four crop rotations were not significantly different in their τ values. These results can be useful to quickly assess the changes in soil physical properties because of crop management practices and make necessary changes to enhance agricultural resilience.