Visually　meaningful　image　encryption　(VMIE)　means　that　a　plain　image　can　be　encrypted　into　a　visually　meaningful　cipher　image　(VMCI),　which　makes　the　secret　more　imperceptible　than　noise-like　cipher　images.　Here,　we　first　present　a　universal　embedding　model　(UEM)　and　further　present　a　new　UEM-based　VMIE　algorithm.　The　plain　image　is　pre-encrypted　and　then　embedded　into　the　integer　wavelet　subbands　of　the　host　image　in　a　dynamic　way.　In　order　to　avoid　the　overflow,　a　threshold　limiting　function　is　used　to　modify　the　range　of　pixel　values　of　the　host　image.　To　adapt　different　types　of　wavelet　transform　subbands,　a　UEM　is　proposed　to　be　used　to　embed　the　secret　information　domain　into　the　host　domain.　Moreover,　in　the　embedding　process,　a　four-dimensional　discrete　chaotic　system　is　used　to　ensure　the　security　of　embedding.　The　numbers　of　embedded　bits　in　the　four　embedded　domains　can　be　adjusted　flexibly.　A　traversal　algorithm　is　designed　to　find　the　optimal　numbers　of　embedded　bits　for　different　types　of　wavelet　transform　in　order　to　achieve　an　optimal　visual　quality　of　cipher　images.　A　matrix-bit-depth-conversion　algorithm　is　designed　where　a　large　matrix　with　low　bit　depth　can　be　transformed　into　a　small　matrix　with　high　bit　depth　to　meet　the　input　requirements　of　UEM,　which　means　that　the　size　of　the　plain　image　is　not　limited　to　a　quarter　of　the　size　of　the　host　image.　Simulation　results　and　performance　comparisons　show　that　the　proposed　VMIE　algorithm　can　achieve　a　better　visual　quality　than　existing　VMIE　algorithms.　©　2021　Elsevier　Inc.