The Twin ANthropogenic Greenhouse Gas Observers (TANGO) mission will monitor and quantify greenhouse gas emissions at the level of individual facilities. A consortium consisting of ISISpace, TNO, SRON and KNMI are developing the TANGO mission for the ESA Scout program. ISISpace is the prime contractor and responsible for the spacecraft, SRON and KNMI are responsible for the atmospheric science, while TNO is developing the instruments. The TANGO space segment consists of two agile 16U CubeSat satellites flying closely in tandem, each equipped with an imaging spectrometer. TANGO Carbon measures the emission of CH₄ and CO₂ in the SWIR1 spectral band (1590-1675 nm at 0.45-nm spectral resolution), while TANGO Nitro measures the emission of NO₂ in the visible spectral range (405- 490 nm at 0.6-nm spectral resolution). Both instruments are reflective pushbroom spectrometers, made almost entirely from aluminum, and will cover a 30-km swath from a 500-km altitude with a spatial resolution of 300 m. The instruments share a similar architecture, using freeform mirrors to achieve high optical performance in a compact 8U envelope. In this paper, we will present the design and performance of the Carbon instrument, where a key engineering challenge is to achieve the desired spatial resolution and SNR from the limited instrument volume (8U). A tight integration of optical and mechanical design, coupled to detailed tolerance, alignment, straylight and STOP (structural thermal optical performance) analyses, allow us to reach that goal.