Textbook explanations of yield curve modelling discuss bootstrapping or other methods. If we take sovereign bonds for deriving the curve, we would get price data from a market data provider like Bloomberg.
However, the prices on a specific date $t$ are actually prices for the settlement date $t+x$ (e.g. $t+1$ or $t+2$ in some countries). Therefore, the curve that results from our model is not a spot curve, but a forward curve. How does one in practice take into consideration this time lag (spot period) for creating spot / zero-coupon curves? I could guess that one uses overnight or repo rates for additional discounting of the bonds, but I would be interested in actual market practice.