The information that is leaked to an eavesdropper during the error reconciliation phase of quantum key distribution (QKD) protocols limits the maximum bit error rate (BER) of a system. In a standard QKD protocol, parity bits are transmitted over an authenticated noiseless channel, to which Eve has access. This Letter presents the concept of using a covert classical communication channel to transmit the parity bits between Alice and Bob without Eve gaining information of the transmitted parity bits. This allows for higher secure key generation rates and operation of a QKD system in which the BER exceeds the limit of the standard protocol. This concept is then applied to a practical free-space optical system that contains multiple parallel channels, where channel loss, crosstalk, atmospheric turbulence effects, and noise are considered.