Although it's possible to bake "bread" without sugar, yeast or high carbohydrates, it won't resemble bread in the traditional sense. Depending on the substitute ingredients involved, the result is usually a pan-shaped loaf with a denser texture than regular bread, not to mention a markedly different flavor. If you follow a low-carb or anti-yeast diet, however, the gustatory tradeoffs may be worth it to gain improved health.
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Bread at its simplest consists of flour, yeast and water. Once a baker has combined those basic ingredients, the yeast -- activated by exposure to moisture -- consumes carbohydrates in the flour and produces carbon dioxide bubbles that inflate the dough. Some recipes call for additional sugar to feed the yeast. Gluten, strands of bonded protein in the dough, forms a lattice of sorts that contains the carbon dioxide bubbles and gives bread its structure. If one of the basic ingredients is missing, the process fails, which creates serious challenges for bread lovers trying to avoid yeast, sugar or carbs.
Strictly speaking, it's impossible to bake bread with zero carbohydrates because the only foods entirely free of carbs are animal products such as meat, poultry and fish, and fats. However, low-carb bakers often use ingredients such as soy flour, finely ground nuts or seeds, and commercial low-carb baking mixes to form the bulk of a low-carb, breadlike loaf. Dana Carpender, author of "500 More Low-Carb Recipes," recommends bran for baked goods as well -- it adds structure and fiber without extra carbohydrates. Low-carb loaves generally have considerably fewer carbs per slice than regular bread. Carpender's recipes, for example, contain 5 to 8 grams of carbohydrate per slice; the carb counts for regular bread usually number in the 20s.
If you're avoiding yeast and yeast products, your go-to ingredients for bread baking are baking soda and baking powder -- chemical leaveners that react with acidic ingredients to produce carbon dioxide. You've probably used baking soda or powder to bake cookies, quick breads, muffins and cakes. These recipes also usually contain eggs to bind the ingredients and provide the internal structure that yeast provides in traditional bread. Note that if you're using baking soda alone as a leavener, you must also include an acid with which it can interact -- buttermilk is common. Baking powder, by contrast, already contains the necessary acids.
You easily can withhold sugar from a traditional bread recipe that calls for it -- since it's probably there to boost yeast action, the result simply will be a loaf that doesn't rise as vigorously. For quick breads that rely on sugar solely for flavor, sugar substitutes will do the trick. You can swap a powdered sucralose product intended for baking cup-for-cup for sugar. Stevia powder, or stevia powder blended with fructooligosaccharide -- FOS -- works as well; stevia/FOS blends are less bitter than stevia alone. Check the substitution ratios on the label because stevia is much sweeter than sugar. Imitation honey and pancake syrups made with sugar alcohols are additional options -- but keep in mind they can cause gas in some people.