Drift tube ion mobility spectrometers (IMS) are widely used for fast trace gas detection in air, but portable compact systems are typically very limited in their resolving power. Decreasing the initial ion packet width improves the resolution, but is generally associated with a reduced signal-to-noise-ratio (SNR) due to the lower number of ions injected into the drift region. In this paper, we present a refined theory of IMS operation which employs a combined approach for the analysis of the ion drift and the subsequent amplification to predict both the resolution and the SNR of the measured ion current peak. This theoretical analysis shows that the SNR is not a function of the initial ion packet width, meaning that compact drift tube IMS with both very high resolution and extremely low limits of detection can be designed. Based on these implications, an optimized combination of a compact drift tube with a length of just 10 cm and a transimpedance amplifier has been constructed with a resolution of 183 measured for the positive reactant ion peak (RIP+), which is sufficient to e.g. separate the RIP+ from the protonated acetone monomer, even though their drift times only differ by a factor of 1.007. Furthermore, the limits of detection (LODs) for acetone are 180 ppt(v) within 1 s of averaging time and 580 pptv within only 100 ms.