We analyze a generic model where wounded quarks are amended with strings in which both endpoint positions fluctuate in spatial rapidity. With the assumption that the strings emit particles independently of one another and with a uniform distribution in rapidity, we are able to analyze the model semi-analytically, which allows for its detailed understanding. Using as a constraint the one-body string emission functions obtained from the experimental data for collisions at √ sNN = 200 GeV, we explore the two-body correlations for various scenarios of string fluctuations. We find that the popular measures used to quantify the longitudinal fluctuations (anm coefficients) are limited with upper and lower bounds. These measures can be significantly larger in the model where both end-point are allowed to fluctuate, compared to the model with single end-point fluctuations.