The meaning of a sentence is determined by the meaning of its parts and the way in which those parts are assembled. This principle of compositionality enables humans to produce and understand new sentences. Then how to derive the meaning of a sentence if there is uncertainty with respect to the meaning of its parts? In this talk, I address two kinds of uncertainty, imprecision and indeterminacy, and use degree expressions to showcase the strategies of dealing with uncertainty in compositional semantics. I start with comparative sentences involving imprecise measurements (i.e., a range of values, instead of a single value). For example, in a sentence like “My giraffe is taller than every tree is”, the comparison is conducted with a range of heights of trees. I show a novel, interval-based, generalized approach to compositionally derive the meaning of comparative sentences in a precise way, even if imprecise measurements are involved. Then I continue with sentences like “Mary is taller than exactly two boys are”. This sentence is puzzling because a local part of the sentence is uninterpretable. “than exactly two boys are” corresponds to an uninterpretable degree question “how tall are exactly two boys”, so it should be uninterpretable as well. I show that this local uninterpretability is due to indeterminacy, and it can be resolved via a delayed evaluation mechanism at the global sentential level. I end with a discussion on how these strategies of dealing with uncertainty go beyond degree expressions and have profound implications for analyzing other linguistic phenomena.