diff --git a/daml-lf/interpreter/src/test/scala/com/digitalasset/daml/lf/speedy/svalue/OrderingSpec.scala b/daml-lf/interpreter/src/test/scala/com/digitalasset/daml/lf/speedy/svalue/OrderingSpec.scala
index 5fb62bf11e..ceadd96202 100644
--- a/daml-lf/interpreter/src/test/scala/com/digitalasset/daml/lf/speedy/svalue/OrderingSpec.scala
+++ b/daml-lf/interpreter/src/test/scala/com/digitalasset/daml/lf/speedy/svalue/OrderingSpec.scala
@@ -447,10 +447,10 @@ class OrderingSpec
     implicit val svalueOrd: Order[SValue] = Order fromScalaOrdering Ordering
     implicit val cidOrd: Order[Cid] = svalueOrd contramap SValue.SContractId
     val EmptyScope: Value.LookupVariantEnum = _ => None
-    "match SValue Ordering" in forAll(genAddend, minSuccessful(100)) { va =>
+    "match SValue Ordering" in forAll(genAddend, minSuccessful(20)) { va =>
       import va.{injarb, injshrink}
       implicit val valueOrd: Order[Value[Cid]] = Tag unsubst Value.orderInstance[Cid](EmptyScope)
-      forAll(minSuccessful(20)) { (a: va.Inj[Cid], b: va.Inj[Cid]) =>
+      forAll(minSuccessful(5)) { (a: va.Inj[Cid], b: va.Inj[Cid]) =>
         import va.injord
         val ta = va.inj(a)
         val tb = va.inj(b)
diff --git a/daml-lf/transaction/src/test/scala/com/digitalasset/daml/lf/value/ValueSpec.scala b/daml-lf/transaction/src/test/scala/com/digitalasset/daml/lf/value/ValueSpec.scala
index 8d65ad2a99..8cea827e09 100644
--- a/daml-lf/transaction/src/test/scala/com/digitalasset/daml/lf/value/ValueSpec.scala
+++ b/daml-lf/transaction/src/test/scala/com/digitalasset/daml/lf/value/ValueSpec.scala
@@ -150,14 +150,10 @@ class ValueSpec
       val EmptyScope: Value.LookupVariantEnum = _ => None
       implicit val ord: Order[T] = Tag unsubst Value.orderInstance(EmptyScope)
 
-      "obeys order laws" in forAll(genAddend, minSuccessful(100)) { va =>
+      "obeys order laws" in forAll(genAddend, minSuccessful(10)) { va =>
         implicit val arb: Arbitrary[T] = va.injarb[Cid] map (va.inj(_))
         checkLaws(SzP.order.laws[T])
       }
-
-      "preserves base order" in forAll(genAddend, minSuccessful(100)) { va =>
-        checkOrderPreserved[Cid](va, EmptyScope)
-      }
     }
 
     "for record and variant types" - {