In　1983,　Burr　and　Erdős　initiated　the　study　of　Ramsey　goodness　problems.　Nikiforov　and　Rousseau　(2009)　resolved　almost　all　goodness　questions　raised　by　Burr　and　Erdős,　in　which　the　bounds　on　the　parameters　are　of　tower　type　since　their　proofs　rely　on　the　regularity　lemma.　Let　Bk,n　be　the　book　graph　on　n　vertices　which　consists　of　n−k　copies　of　Kk+1　all　sharing　a　common　Kk,　and　let　H=Kp(a1,…,ap)　be　the　complete　p-partite　graph　with　parts　of　sizes　a1,…,ap.　Recently,　avoiding　use　of　the　regularity　lemma,　Fox,　He　and　Wigderson　(2023)　revisit　several　Ramsey　goodness　results　involving　books.　They　comment　that　it　would　be　very　interesting　to　see　how　far　one　can　push　these　ideas.　In　particular,　they　conjecture　that　for　all　integers　k,p,t≥2,　there　exists　some　δ＞0　such　that　for　all　n≥1,　1≤a1≤⋯≤ap−1≤t　and　ap≤δn,　we　have　r(H,Bk,n)=(p−1)(n−1)+dk(n,Ka)+1,　where　dk(n,Ka)　is　the　maximum　d　for　which　there　is　an　(n+d−1)-vertex　Ka-free　graph　in　which　at　most　k−1　vertices　have　degree　less　than　d.　They　verify　the　conjecture　when　a1=a2=1.　We　disprove　the　conjecture　of　Fox　et　al.　(2023).　Building　upon　the　work　of　Fox　et　al.,　we　make　a　substantial　step　by　showing　that　for　every　k,p,t≥2,　there　exists　δ＞0　such　that　the　following　holds　for　all　large　n.　Let　1≤a1≤…≤ap−1≤t　and　ap≤δn　be　positive　integers.　If　a1=1,　then　r(H,Bk,n)≤(p−1)(n−1)+k(p−1)(a2−1)+1.　The　inequality　is　tight　if　a2|(n−1−k).　Moreover,　we　prove　that　for　every　k,a≥1　and　p≥2,　there　exists　δ＞0　such　that　for　all　large　n　and　b≤δln⁡n,　r(Kp(1,a,b,…,b),Bk,n)=(p−1)(n−1)+k(p−1)(a−1)+1　if　a|(n−1−k),　where　the　case　when　a=1　has　been　proved　by　Nikiforov　and　Rousseau　(2009)　using　the　regularity　lemma.　The　bounds　on　1/δ　we　obtain　are　not　of　tower-type　since　our　proofs　do　not　rely　on　the　regularity　lemma.　©　2023　Elsevier　Inc.