It doesn’t look like I will be able to use the Tslim pump. I need basal rates as small as .050 and .075. The Tandem pump only does 0.1. I guess I might have to wait for medtronic’s 780.
Does your body respond differently to zero and 0.05 unit?
Most pumps including Tslim have basal suspension features. Although whether that can be scheduled on an automatic daily basis or not is something I don’t know. (I do know latest Tslims support automatic basal suspend based on CGMS readings but that’s probably different than what you want.)
I see my diabetes educator on Thursday. I will see what she says. My husband was trying to work something out for me like giving me 0 units for 2 hours and then make some up in the next 2 but I don’t think that would work. It suspends at 4.4 mmol. That is a bit too low for me. I am somewhat dissappointed. I might have to wait a little longer for Medtronic’s 780 to be released.
Another option especially if all your doses are small is to use diluted insulin. Pharmacists are able to do this but it is likely off-label usage for your pump.
If they dilute U-100 insulin down to U-20, and you use that in your pump, you can then set the pump for .25 units an hour and of that .25 units of diluted insulin delivered, only 0.05 units are actual insulin.
Here’s an an actual medical journal article on using diluted insulin in pumps: Challenges in Delivering Smaller Doses of Insulin - PMC
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Don’t give up yet. Babies use the t-slim, so I’m guessing your CDE will be able to make it work for you if it’s what you really want. 
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Gee, I hope you’re right. My husband was trying to adjust my basal rate so that I would get enough insulin for 2 hours and then reduce the next 2 hours to make the amount that I need as so on. I find it confusing, especially if I need an adjustment.
When my son started on T-Slim during honeymoon he also needed very little basal. Using diluted insulin is a common solution for kids, but we found in practice we didn’t need to go there. Just as your husband was trying, we set his pump to alternate between 0.1 and 0 units, commonly referred to as zig-zag basal.
The biggest limitation when doing this is that the pump (at least on the firmware for G5 connection) only allows 14 basal rate start-times, so you can’t set the zig-zag to short intervals. Fortunately he needed no basal insulin at all overnight so we didn’t need more intervals than that. In your situation, diluted insulin might be a better solution.
Yeah, it might be.
D’Etta Meloche