There are numerous ways to thicken a sauce (made from scratch or from a deglaze) without using a roux. Such as:

Beurre Manié

(Pronounced burr mahnyay): mix equal quantities of butter and flour together to form a smooth paste. Add small pieces, stirring rapidly with a wire whisk to dissolve until the sauce reaches the right consistency. Be sure to simmer the sauce for a few minutes to cook the flour. The melted butter will add a sheen and much flavor to the sauce.

Waxy Maize

Add waxy maize to a cup, add cold water and whisk to a smooth consistency. Add the mixture to a sauce and bring to a boil, stirring continuously until the sauce thickens. Remove from the heat. Ideal for sauces that are to be frozen as it does not congeal as much when defrosted.

Cornstarch

Add cornstarch to a cup, add cold water and whisk to a smooth consistency. Add the mixture to a sauce and bring to a boil, stirring continuously to produce an almost clear, glossy sauce. If you overcook a sauce thickened with cornstarch, the heat will breakdown the cornstarch and the sauce will become thin again. Flour has only half the strength of cornstarch as a thickening agent.

Arrowroot

Use the same method as that used for cornstarch to produce an even clearer sauce. Arrowroot is used less than cornstarch because it tends to be more expensive. (It’s worth the price, though)

Kudzu

Kudzu is starch extracted from a vine. It needs to be mixed with water and stirred to a smooth consistency before being added to sauces. It will thicken at room temperature. Most commonly available in health food stores and Japanese food stores.

Bread Crumbs

A very effective thickener, as the starch has already been cooked, but best used where a smooth consistency is not important.

Egg yolk and heavy cream

Egg yolks can be used as a thickener, but they have only limited thickening power and they’re tricky to work with because they will curdle if over-heated. Sometimes they are beaten with heavy cream to raise their curdling temperature, but even so, it’s still well below boiling point. A little too rich for my taste.

Vegetable purées

Adding a purée of one or more of the main ingredients can thicken a vegetable sauce. I find it best to pour these through a fine-mesh strainer before adding them to a sauce or they have a somewhat pulpy texture.

Reduction

To avoid using a starch altogether, a sauce can be thickened by reducing it, allowing it to cook long enough to evaporate some of the water. But it needs to be taken into account that if the sauce is strongly flavored before beginning the reduction, it will gain in intensity as the water evaporates and the solids are left.

Note: There is one other I didn't really want to mention, but it is a valid method. It's called "whitewash" - a thin mixture of flour and water. It leaves a gritty texture. Not nice.

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