This paper examines the low-probability-of-exploitation (LPE) characteristics of a noncontiguous orthogonal frequency division multiplexing (NC-OFDM) system. NC-OFDM transmission is similar to OFDM transmission but only uses a subset of the frequencies either to avoid incumbent transmissions or due to tactical considerations. This paper considers an NC-OFDM transmission with a given set of active subcarriers and examines how an eavesdropper can infer transmission parameters such as total duration of an NC-OFDM symbol, length of the cyclic prefix, etc., using tools like the cyclostationary analysis. Such an analysis reveals that difficulty in estimating the total nominal bandwidth of NC-OFDM transmissions (bandwidth that includes frequencies occupied by inactive subcarriers) poses a fundamental challenge in determining the correct sampling rate and the subsequent retrieval of the transmitted signal. The analysis also shows that the features of the cyclic autocorrelation function (CAF) of an NC-OFDM transmission depend closely on the set of active subcarriers. Procedures for inferring the transmission parameters from the CAF are discussed while noting that the choice of an interleaved set of subcarriers introduces additional ambiguity in determining the transmission parameters. A PCA-based offline timing recovery scheme is proposed and used as a guidepost in determining the minimum rate at which an active set of subcarriers must be refreshed to avoid easy exploitation. Finally, key advantages of an NC-OFDM system over an OFDM system from an LPE-standpoint are discussed and suggestions for an LPE-centric design of NC-OFDM systems are made.