Reducing hash output length

I am using output of (keyed) hash function to make sure the input was not modified, I store it along with input. Now output of SHA-1 is 20 bytes. Say I want to reduce the output. And have it output 10 bytes - I know I can truncate it (e.g., just take first 10 bytes of 20 bytes).

But my question is: how much can I truncate output so that it is still reasonably secure? (assuming like I said I use this for verification, e.g., make sure string that I hashed didn't change).

Can I reduce it to 8 bytes say? Is it still reasonably secure? (for my needs)