Summary: In the context of quantum gravitational systems, we place bounds on regions in field space with slowly varying positive potentials. Using the fact that \(V < \Lambda_s^2\), where \(\Lambda_s(\phi)\) is the species scale, and the emergent string conjecture, we show this places a bound on the maximum diameter of such regions in field space: \(\Delta\phi \leq a\log(1/V) + b\) in Planck units, where \(a \leq \sqrt{(d - 1)(d - 2)}\), and \(b\) is an \(\mathcal{O}(1)\) number and expected to be negative. The coefficient of the logarithmic term has previously been derived using TCC, providing further confirmation. For type II string flux compactifications on Calabi-Yau threefolds, using the recent results on the moduli dependence of the species scale, we can check the above relation and determine the constant \(b\), which we verify is \(\mathcal{O}(1)\) and negative in all the examples we studied.