I once was interested in AD9850 (or was it AD9852?)
It also has a current input for setting the amplitude and with a (DC) DAC it could be regultated to quite low values, but this is not good practice.
Better is to have an amplitude range in some limited range, and then use some attenuators after the signal is generated. These also attenuate noise, and maintain a decent sine wave.
You only need a few of these. For example a -10dB, a -20dB and a -40dB relais based attenuators, get you down to -70dB without loosing signal quality. And you only use the amplitude control to fill in the gaps between the attenuators.