diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 01c43486f800f..604fd9256e10f 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -153,7 +153,7 @@ Deprecations
 
 Performance improvements
 ~~~~~~~~~~~~~~~~~~~~~~~~
--
+- Performance improvement when indexing with more than 4 keys (:issue:`54550`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index e974b5d0eec46..5c7680bc6fb6c 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -375,7 +375,7 @@ cdef class IndexEngine:
         # map each starget to its position in the index
         if (
                 stargets and
-                len(stargets) < 5 and
+                len(stargets) < (n / (2 * n.bit_length())) and
                 not na_in_stargets and
                 self.is_monotonic_increasing
         ):