Amphiphile adsorption at the air/water interface lowers the surface tension (gamma) of the solution. After a critical surfactant concentration (C), gamma becomes constant (with a break in the gamma-log C plot), which is considered the critical micelle concentration (CMC). At very low amphiphile concentration, gamma decreases slowly, forming a plateau, then decreases sharply and often nonlinearly by a co-operative adsorption process till the second plateau is reached at CMC. To get the Gibbs surface excess (Gamma) of the amphiphile relative to water, a polynomial equation of appropriate degree needs to be used, since the drop in gamma progresses with continuous changing slope, which maximizes at CMC and becomes zero afterward. Recent research has evidenced that a complete saturated Gibbs monolayer may not always form at CMC; there may be formation of multilayer of micelles below the Gibbs monolayer, which cannot be assessed by ST measurements. A method like neutron reflectometry (NR) can evaluate the Gamma beyond CMC. A procedure for determining Gamma(max) from tensiometric results is herein proposed. Amphiphiles do sometimes show a linear decline in gamma with log C followed by a break with a plateau at CMC. There, a single slope leading to a single surface excess quantity is obtained for the Gibbs equation at all concentrations up to CMC. Possible reasons for such results are given. Current conflicting ideas and criticisms on the issue of Gibbs equation and determination of Gamma and Gamma(max), have been addressed. (C) 2012 Elsevier Inc. All rights reserved.