I think exposure compensation is not to be worked after a recipe, but by thorough understanding of what happens. When setting a negative value at the same time as higher ISO, it is an invitation to underexposure, where shadow detail is drenched in noise.
But it must also be better understood, that raising ISO will decrease dynamic range, so that not so much dynamic can be caught on the sensor before it saturates and clips highlights.
So if the dynamic range of the scene is larger than the actual dynamic range of the sensor, something will be lost, either shadow, highlight or both. It is up to the photographer to decide whether to lose anything and in what region - highlight, shadow or both. Applying a constant -0.7 exposure compensation is telling your camera that you want the image to be darker than the metering system suggests. If the reason is that ISO has been raised so much that something must be lost, it is also a choice toward losing at the shadow side, drenching the details there in noise.
ISO setting does not alter the sensitivity of the sensor. It only governs the amplification of its signal, as well as noise. Raising amplification may push highlights into clipping, when the dynamic range of the scene is greater than what the sensor can capture at a given ISO setting. Highlight detail may be saved with a high ISO setting at the price of lost shadow detail, by setting negative compensation.