The counterion condensation theory originally proposed by Manning is extended to take account of both finite counterion concentration ( m C) and the actual structure of the array of discrete changes. Counterion condensation is treated here as a binding isotherm problem, in which the unknown free volume is replaced by an unknown local binding constant β′, which is expected to vary with m C and polyion structure. The relation between the condensed fraction of counterion charge, r, β′ and m C is obtained from the relevant grand partition function via the maximum term method. In the case of the single polyion in a large salt reservoir, the result is practically identical to Manning's equation. In order to determine the values of β′ and r at arbitrary m C, a second relation between r, β′ and m C is required. We propose an alternative auxiliary relation that is equivalent to previous assumptions near m C=0, but which yields qualitatively correct and quantitatively useful results at finite m C. Simple expressions for r vs. m C and β′ vs. m C are obtained by simultaneously solving the binding isotherm and auxiliary equations. Then r and β′ are evaluated for five different linear arrays of infinite extent with different geometries: (1) a straight line of charges with uniform axial spacing; (2) two parallel lines of in-phase uniformly spaced charges; (3) a single-helix of discrete charges with uniform axial spacing; (4) a double-helix of discrete charges with uniform axial spacing of pairs of charges; (5) a cylindrical array of many parallel charged lines, chosen to simulate a uniformly charged cylinder. In all cases, the computed binding isotherms exhibit qualitatively correct behavior. As m C approaches zero, r approaches the Manning limit, r=1−1/( L B/ b) where b is the average axial spacing of electronic charges in the array and L B is the Bjerrum length. However, β′ varies with polyion geometry, even in the zero salt limit, and matches the Manning value only in the case of a single straight charged line. With increasing m C, r declines significantly below its limiting value whenever λ b≳0.3, where λ is the Debye screening parameter. In the case of cylindrical arrays containing either 2 or 100 parallel charged lines, r also decreases, whenever λ d≳2.0, where d is the diameter of the array. In the case of two parallel charged lines, each with axial charge spacing b=3.4 Å, which are separated by d=200 Å, r exhibits a plateau value, 0.76, characteristic of the two combined lines, when λ d≪2.0, and declines with increasing m C to a shelf value, 0.52, characteristic of either single line, when λ d≳2.0 and the lines become effectively screened from one another. β′ behaves in a roughly similar fashion. In the case of a cylindrical array of charged lines with the diameter and linear charge density of DNA, the r-values predicted by the present theory agree fairly well with those predicted by non-linear Poisson–Boltzmann theory up to 0.15 M uni-univalent salt.