Hi @Ldr1970 and thanks for the information. Here is my feedback. The first two captures look as I would expect. Your Joulescope is correctly autoranging to the most sensitive 18 µA range with nothing connected. Your DUT appears to be drawing 1.34 mA in figure 3, and your Joulescope autoranged to the 18 mA range, which is fine. It probably could autorange down to the 1.8 mA range for improved resolution and lower noise. However, this is the defect that I hinted at earlier, but your Joulescope still makes correct measurements, just with worse resolution and noise than it could have.
On figure 4, we have a misunderstanding:
Your Joulescope is actually saturating at the maximum value for the range, which is why standard deviation (σ) is zero. If your device is still drawing 1.3 mA with Joulescope’s 1000 Ω shunt resistor in the 18 µA range, the voltage drop across Joulescope is 1.3 mA * 1000 = 1.3V, meaning your target only sees 3.14 V - 1.3V = 1.84V, which may make your target brown out.
The last figure looks like Joulescope is working correctly. Unfortunately, JLS capture files are currently truncated to increments of 0.2 seconds. Your capture has 0.199 seconds, which means the file has no data 
I first noted this issue here.
I have a few requests:
- Could you try again to collect a capture between 0.2 seconds and 0.5 seconds long and then post the capture?
- Are you sure that your device is going into its lowest power 16 µA sleep mode? It’s probably worth double-checking using your previous test method while Joulescope is also connected.
Thank you!