Motivated by the shortcomings of the yield curve method used by the Kazakhstan Stock Exchange (KASE), we designed an algorithmic method of constructing a yield curve in a market with low and variable liquidity. We chose Nelson-Seigel as a curve and the ten most recent transactions in each subrange of maturity as the data. Both decisions stemmed from the constraints of an illiquid and inefficient market. The parsimony and rigidity of Nelson-Seigel proved useful when trades are few and prices are far apart. The choice of sampling is meant to produce enough sufficiently spaced observations, albeit at the expense of synchronicity. To provide the user better context for the curve and enable informed interpretation, we recommend supplementing the curves and their parameters with metrics of fit and age of the sample. Using the data from KASE, we computed the curve for each week starting from mid-2010 to end-2018 and made the results publicly available to provide access to interest rate data for analysts and to facilitate macroeconomic research.