Method for increasing in a baked product, after baking, the level of water-soluble arabinoxylan with an average degree of polymerization ranging from 5 to 50, preferably ranging from 5 to 35, more preferably ranging from 5 to 25, said method comprising the steps of: - (a) Preparing a dough for a baked product with flour, with a mixture of flours, with a mixture of one or more milling fraction(s) comprising at least 40% (w/w), preferably at least 50%, more preferably at least 60%, most preferably at least 70% of flour derived from wheat, or with a mixture of flour(s) and milling fractions, said flour or mixture having a total arabinoxylan content of at least 2.5% (w/w, % of dry weight), and adding to said dough an enzyme preparation comprising at least one thermophilic endoxylanase in an amount at least 2-fold higher, preferably at least 3 to 6 times higher or even 10 times higher than the dose conferring 90% of the maximal bread volume increase obtained by addition of such enzyme preparation to the recipe of said baked product; or - (b) Preparing a dough for a baked product with flour, with a mixture of flours, with a mixture of one or more milling fraction(s), or with a mixture of flour(s) and milling fractions, said flour or mixture having a total arabinoxylan content of at least 2% (w/w, % of dry weight), and adding to said dough an enzyme preparation comprising (i) at least one thermophilic endoxylanase in an amount at least 2-fold higher, preferably at least 3 to 6 times higher or even 10 times higher than the dose conferring 90% of the maximal bread volume increase obtained by addition of such enzyme preparation to the recipe of said baked product and (ii) at least one endoxylanase highly selective for water-unextractable arabinoxylan; - wherein said thermophilic endoxylanase is an endoxylanase enzyme whose optimal temperature for activity is at least 65°C. - (a) Preparing a dough for a baked product with flour, with a mixture of flours, with a mixture of one or more milling fraction(s) comprising at least 40% (w/w), preferably at least 50%, more preferably at least 60%, most preferably at least 70% of flour derived from wheat, or with a mixture of flour(s) and milling fractions, said flour or mixture having a total arabinoxylan content of at least 2.5% (w/w, % of dry weight), and adding to said dough an enzyme preparation comprising at least one thermophilic endoxylanase in an amount at least 2-fold higher, preferably at least 3 to 6 times higher or even 10 times higher than the dose conferring 90% of the maximal bread volume increase obtained by addition of such enzyme preparation to the recipe of said baked product; or - (b) Preparing a dough for a baked product with flour, with a mixture of flours, with a mixture of one or more milling fraction(s), or with a mixture of flour(s) and milling fractions, said flour or mixture having a total arabinoxylan content of at least 2% (w/w, % of dry weight), and adding to said dough an enzyme preparation comprising (i) at least one thermophilic endoxylanase in an amount at least 2-fold higher, preferably at least 3 to 6 times higher or even 10 times higher than the dose conferring 90% of the maximal bread volume increase obtained by addition of such enzyme preparation to the recipe of said baked product and (ii) at least one endoxylanase highly selective for water-unextractable arabinoxylan; - wherein said thermophilic endoxylanase is an endoxylanase enzyme whose optimal temperature for activity is at least 65°C.