Our Gemara on Amud Beis tells us that decorations in the Succah do not invalidate height requirements but they do invalidate width requirements. That is, the minimum height of a Succah is 10 tefachim, and even if some of that is used up by decorations that is not reducing the space. However, the minimum width is seven tefachim, and decorations will reduce that space.

The commentaries try to understand what is the technical difference between height and weight. Why decorations use up the space in width but not in height. See Tosafos here and acharonim for more details.

However, I cannot resist offering a chassidish interpretation to this statement: “⁦Sukkah decorations do not diminish the height of the sukka. However, decorations that are spread on the side diminish the area.” 

This suggests if you want to enhance your mitzvah observance and take on stringencies, make sure they are only between you and God. That is represented by the height. However, if the stringencies interferes with the people on your right on your left, that is the people that love with you, it is indeed posul.

This derash might seem far-fetched but as we will see in the upcoming dappim, even the Rama in Toras Haolah (see for example III:62), aside from of course chassidish rebbes, saw incredible symbolism in the laws of Succah.