diff --git a/build/starship/build.sh b/build/starship/build.sh
index 1dc6b977d..f3530c26c 100755
--- a/build/starship/build.sh
+++ b/build/starship/build.sh
@@ -29,6 +29,9 @@ BUILD_DEPENDS_IPS="
 
 SKIP_SSP_CHECK=1
 
+# starship contains BMI instructions even when built on an older CPU
+BMI_EXPECTED=1
+
 CARGO_ARGS="--no-default-features"
 
 set_arch 64
diff --git a/build/valgrind/build.sh b/build/valgrind/build.sh
index 80e64f295..3901c8f52 100755
--- a/build/valgrind/build.sh
+++ b/build/valgrind/build.sh
@@ -32,6 +32,9 @@ CTF_FLAGS+=" -s"
 
 NO_SONAME_EXPECTED=1
 
+# valgrind contains BMI instructions even when built on an older CPU
+BMI_EXPECTED=1
+
 # valgrind configure requires GNU tools
 export PATH=$GNUBIN:$PATH