diff --git a/app/finders/projects_finder.rb b/app/finders/projects_finder.rb
index 42a15234e57..ac18c17dc61 100644
--- a/app/finders/projects_finder.rb
+++ b/app/finders/projects_finder.rb
@@ -79,7 +79,7 @@ class ProjectsFinder < UnionFinder
     elsif min_access_level?
       current_user.authorized_projects(params[:min_access_level])
     else
-      if private_only?
+      if private_only? || impossible_visibility_level?
         current_user.authorized_projects
       else
         Project.public_or_visible_to_user(current_user)
@@ -96,6 +96,30 @@ class ProjectsFinder < UnionFinder
     end
   end
 
+  # This is an optimization - surprisingly PostgreSQL does not optimize
+  # for this.
+  #
+  # If the default visiblity level and desired visiblity level filter cancels
+  # each other out, don't use the SQL clause for visibility level in
+  # `Project.public_or_visible_to_user`. In fact, this then becames equivalent
+  # to just authorized projects for the user.
+  #
+  # E.g.
+  # (EXISTS(<authorized_projects>) OR projects.visibility_level IN (10,20))
+  #   AND "projects"."visibility_level" = 0
+  #
+  # is essentially
+  # EXISTS(<authorized_projects>) AND "projects"."visibility_level" = 0
+  #
+  # See https://gitlab.com/gitlab-org/gitlab/issues/37007
+  def impossible_visibility_level?
+    return unless params[:visibility_level].present?
+
+    public_visibility_levels = Gitlab::VisibilityLevel.levels_for_user(current_user)
+
+    !public_visibility_levels.include?(params[:visibility_level])
+  end
+
   def owned_projects?
     params[:owned].present?
   end
diff --git a/changelogs/unreleased/projects_finder_visibility_optimization.yml b/changelogs/unreleased/projects_finder_visibility_optimization.yml
new file mode 100644
index 00000000000..9d6d626d5cb
--- /dev/null
+++ b/changelogs/unreleased/projects_finder_visibility_optimization.yml
@@ -0,0 +1,5 @@
+---
+title: Optimize query when Projects API requests private visibility level
+merge_request: 20594
+author:
+type: performance