We present a new method of constructing Condorcet domains from pairs of Condorcet domains of smaller sizes (concatenation - shuffle scheme). The concatenation - shuffle scheme provides maximal, connected, copious, peak-pit domains whenever the original domains have these properties. It allows to construct maximal peak-pit Condorcet domains that are larger than those obtained by the Fishburn’s alternating scheme for all n>=13 alternatives. For a large number n of alternatives, we get a lower bound 2.1045^n for the cardinality of the largest peak-pit Condorcet domain and a lower bound 2.1890^n for the cardinality of the largest Condorcet domain, improving Fishburn’s result. We also show that all Arrow’s single-peaked domains can be constructed by concatenation - shuffle scheme starting from the trivial domain.