  We study the problem of the execution of a moderate size order in an illiquid
market within the framework of a solvable Markovian model. We suppose that in
order to avoid impact costs, a trader decides to execute her order through a
unique trade, waiting for enough liquidity to accumulate at the best quote. We
find that despite the absence of a proper price impact, such trader faces an
execution cost arising from a non-vanishing correlation among volume at the
best quotes and price changes. We characterize analytically the statistics of
the execution time and its cost by mapping the problem to the simpler one of
calculating a set of first-passage probabilities on a semi-infinite strip. We
finally argue that price impact cannot be completely avoided by conditioning
the execution of an order to a more favorable liquidity scenario.
