The Green–Ampt expression for determining field-saturated hydraulic conductivity (Kfs) and matric flux potential (ϕm) from falling-head ring infiltrometer measurements produces a singularity when the standpipe cross-section divided by the ring cross-section (R) equals the change in porous medium water content (Δθ). As R = Δθ is clearly possible in wet, low-permeability materials, the objective of this study was to develop an alternative falling-head ring infiltrometer analysis that applies for 0 < R < +∞, including R = Δθ. This was accomplished by replacing the natural logarithm in the Green–Ampt analysis with a Taylor series expansion, which removes the (R − Δθ) divisor from the analysis. The Taylor series form of the Green–Ampt expression collapses to a simple algebraic expression when R = Δθ. Combining this algebraic expression with a similar analysis developed for gravitationless infiltration provides an improved approximate relationship for estimating Kfs when standpipe drawdown is small and R < Δθ.