Smooth low level fading of LED strip using PWM with 8-bit ATtiny85

tdeanos:
Is there a way to increase the resolution of the fading at low levels using an 8 bit controller or do I need to get a microcontroller with 16bit PWM?

What, fading only one channel?

Do it in software - what else are you going to use the Tiny85 for?

Your code looks convoluted to me. To implement an exponential fade, just multiply by a factor at each step using a shift-and-add (or shift-and subtract) routine which is going to be faster than a formal multiply. You could use a fixed step of 1.125 or 0.875. You can detect when the result is no longer changing.