I am aware that using a counter or a random value are both acceptable ways of generating nonces, depending on the circumstances.
The tradeoff with using a counter is the necessity to keep state and sometimes this can be a complex problem on its own.
The tradeoff with using a randomly generated nonce is the possibility (even if perhaps astronomically low) of generating the same nonce twice. Please note that I am aware that there are some cryptographic functions that are designed to be resistant to nonce reuse.
Assuming I'm not confident in my system's ability to reliably keep track of a counter, that I am not using a cryptographic function that's resistant to nonce reuse and that I am not assured in leaving nonce generation up to a PRNG, would I be able to significantly lower the probability of nonce reuse if I implemented both a counter as well as a random nonce, compared to the case that I either (xor) use a counter or a random nonce?