We study samples \(\Gamma = (\Gamma_1, \ldots, \Gamma_n)\) of length \(n\) where the letters \(\Gamma_i\) are independently generated according to the geometric distribution \(\mathbb{P}(\Gamma_j = i) = pq^{i-1}\), for \(1 \leq j \leq n\), with \(p+q=1\) and \(0<p<1\). An \({up-smooth\; sample}\) \(\Gamma\) is a sample such that \(\Gamma_{i+1}- \Gamma_i \leq 1\). We find generating functions for the probability that a sample of \(n\) geometric variables is up-smooth, with or without a specified first letter. We also extend the up-smooth results to words over an alphabet of \(k\) letters and to compositions of integers. In addition, we study smooth samples \(T\) of geometric random variables, where the condition now is \(|\Gamma_{i+1}- \Gamma_i| \leq 1\).