diff --git a/src/Rings/groebner.jl b/src/Rings/groebner.jl
index 24a42d84248c..77c4a3a3677a 100644
--- a/src/Rings/groebner.jl
+++ b/src/Rings/groebner.jl
@@ -158,57 +158,61 @@ function standard_basis(I::MPolyIdeal; ordering::MonomialOrdering = default_orde
     return I.gb[ordering]
   end
   if algorithm == :default && is_f4_applicable(I, ordering)
-      groebner_basis_f4(I, complete_reduction=true)
+    #  since msolve v0.7.0 is most of the time more efficient
+    #  to compute a reduced GB by default
+    groebner_basis_f4(I, complete_reduction=true)
   else
-      if algorithm == :default
-          algorithm = :buchberger
+    if algorithm == :default
+        algorithm = :buchberger
+    end
+    if algorithm == :buchberger
+      if !haskey(I.gb, ordering)
+        I.gb[ordering] = _compute_standard_basis(I.gens, ordering, complete_reduction)
+      elseif complete_reduction == true
+        I.gb[ordering] = _compute_standard_basis(I.gb[ordering], ordering, complete_reduction)
       end
-      if algorithm == :buchberger
-        if !haskey(I.gb, ordering)
-          I.gb[ordering] = _compute_standard_basis(I.gens, ordering, complete_reduction)
-        elseif complete_reduction == true
-          I.gb[ordering] = _compute_standard_basis(I.gb[ordering], ordering, complete_reduction)
-        end
-      elseif algorithm == :fglm
-        _compute_groebner_basis_using_fglm(I, ordering)
-      elseif algorithm == :hc
-        standard_basis_highest_corner(I, ordering=ordering)
-      elseif algorithm == :hilbert
-        weights = _find_weights(gens(I))
-        if !any(iszero, weights)
-          J, target_ordering, hn = I, ordering, nothing
-        else
-          R = base_ring(I)
-          K = iszero(characteristic(R)) && !haskey(I.gb, degrevlex(R)) ? _mod_rand_prime(I) : I
-          S = base_ring(K)
-          gb = groebner_assure(K, degrevlex(S))
-          # 2024-02-09 Next lines "blindly" updated to use new homogenization UI
-          H = homogenizer(S, "w")
-          K_hom = H(K)
-          gb_hom = IdealGens(H.(gens(gb)))
-          gb_hom.isGB = true
-          K_hom.gb[degrevlex(S)] = gb_hom
-          singular_assure(K_hom.gb[degrevlex(S)])
-          hn = hilbert_series(quo(base_ring(K_hom), K_hom)[1])[1]
-          H2 = homogenizer(R, "w")
-          J = H2(I)
-          weights = ones(Int, ngens(base_ring(J)))
-          target_ordering = _extend_mon_order(ordering, base_ring(J))
-        end
-        GB = groebner_basis_hilbert_driven(J, destination_ordering=target_ordering,
-                                           complete_reduction=complete_reduction,
-                                           weights=weights,
-                                           hilbert_numerator=hn)
-        if base_ring(I) == base_ring(J)
-          I.gb[ordering] = GB
-        else
-          DH2 = dehomogenizer(H2)
-          GB_dehom_gens = DH2.(gens(GB))
-          I.gb[ordering] = IdealGens(GB_dehom_gens, ordering, isGB = true)
-        end
-      elseif algorithm == :f4
-        groebner_basis_f4(I, complete_reduction=true)
+    elseif algorithm == :fglm
+      _compute_groebner_basis_using_fglm(I, ordering)
+    elseif algorithm == :hc
+      standard_basis_highest_corner(I, ordering=ordering)
+    elseif algorithm == :hilbert
+      weights = _find_weights(gens(I))
+      if !any(iszero, weights)
+        J, target_ordering, hn = I, ordering, nothing
+      else
+        R = base_ring(I)
+        K = iszero(characteristic(R)) && !haskey(I.gb, degrevlex(R)) ? _mod_rand_prime(I) : I
+        S = base_ring(K)
+        gb = groebner_assure(K, degrevlex(S))
+        # 2024-02-09 Next lines "blindly" updated to use new homogenization UI
+        H = homogenizer(S, "w")
+        K_hom = H(K)
+        gb_hom = IdealGens(H.(gens(gb)))
+        gb_hom.isGB = true
+        K_hom.gb[degrevlex(S)] = gb_hom
+        singular_assure(K_hom.gb[degrevlex(S)])
+        hn = hilbert_series(quo(base_ring(K_hom), K_hom)[1])[1]
+        H2 = homogenizer(R, "w")
+        J = H2(I)
+        weights = ones(Int, ngens(base_ring(J)))
+        target_ordering = _extend_mon_order(ordering, base_ring(J))
+      end
+      GB = groebner_basis_hilbert_driven(J, destination_ordering=target_ordering,
+                                         complete_reduction=complete_reduction,
+                                         weights=weights,
+                                         hilbert_numerator=hn)
+      if base_ring(I) == base_ring(J)
+        I.gb[ordering] = GB
+      else
+        DH2 = dehomogenizer(H2)
+        GB_dehom_gens = DH2.(gens(GB))
+        I.gb[ordering] = IdealGens(GB_dehom_gens, ordering, isGB = true)
       end
+    elseif algorithm == :f4
+      #  since msolve v0.7.0 is most of the time more efficient
+      #  to compute a reduced GB by default
+      groebner_basis_f4(I, complete_reduction=true)
+    end
   end
   return I.gb[ordering]
 end