diff --git a/R/data.R b/R/data.R
index 6dcd25c..8975a63 100644
--- a/R/data.R
+++ b/R/data.R
@@ -510,9 +510,16 @@ upset_data = function(
             unique(unlist(intersections_members)),
             NOT_IN_KNOWN_SETS
         )
+        provided_intersection_sizes = sapply(intersections_members, length)
+        provided_intersection_sizes[intersections_members == NOT_IN_KNOWN_SETS] = 0
 
         # TODO: this is slow and memory hungry; ideally we would only get the relevant intersection straight away!
-        possible_intersections = all_intersections_matrix(intersect, NULL, 0, Inf)
+        possible_intersections = all_intersections_matrix(
+          intersect,
+          NULL,
+          min(provided_intersection_sizes),
+          max(provided_intersection_sizes)
+        )
 
         relevant_intersections = rownames(possible_intersections[
             rowSums(possible_intersections[, sets_from_manual_intersections]) > 0,
@@ -1057,4 +1064,4 @@ create_upset_abc_example = function() {
             rep(F, 2)
         )
     )
-}
\ No newline at end of file
+}