diff --git a/src/nlsolve.jl b/src/nlsolve.jl
index 957bac52a5..e9cd460f9d 100644
--- a/src/nlsolve.jl
+++ b/src/nlsolve.jl
@@ -55,6 +55,7 @@ function _inverse_retract_nlsolve(
         retract!(M, F, p, project(M, p, X), retraction; kwargs...)
         project_point && project!(M, q, q)
         F .-= q
+        project_point && project!(M, F, F)
         return F
     end
     isdefined(Manifolds, :NLsolve) ||
diff --git a/test/groups/special_euclidean.jl b/test/groups/special_euclidean.jl
index eedbab4575..ca8730ca97 100644
--- a/test/groups/special_euclidean.jl
+++ b/test/groups/special_euclidean.jl
@@ -78,6 +78,7 @@ Random.seed!(10)
                     X_pts;
                     test_diff=true,
                     diff_convs=[(), (LeftAction(),), (RightAction(),)],
+                    atol=1e-9,
                 )
             end
         end
diff --git a/test/manifolds/rotations.jl b/test/manifolds/rotations.jl
index 66701f17b0..c9055c82c4 100644
--- a/test/manifolds/rotations.jl
+++ b/test/manifolds/rotations.jl
@@ -116,7 +116,7 @@ include("../utils.jl")
                 point_distributions=[ptd],
                 tvector_distributions=[tvd],
                 basis_types_to_from=basis_types,
-                exp_log_atol_multiplier=20,
+                exp_log_atol_multiplier=80,
                 retraction_atol_multiplier=12,
                 test_inplace=true,
             )