diff --git a/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala b/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
index efecdb7071..a2085e2cbf 100644
--- a/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
+++ b/kernel-laws/shared/src/test/scala/cats/kernel/laws/LawTests.scala
@@ -314,9 +314,6 @@ class Tests extends TestsConfig with AnyFunSuiteLike with FunSuiteDiscipline wit
   checkAll("Hash[Queue[Int]", HashTests[Queue[Int]].hash)
 
   {
-    // default Arbitrary[BigDecimal] is a bit too intense :/
-    implicit val arbBigDecimal: Arbitrary[BigDecimal] =
-      Arbitrary(arbitrary[Double].map(n => BigDecimal(n.toString)))
     checkAll("Order[BigDecimal]", OrderTests[BigDecimal].order)
     checkAll("CommutativeGroup[BigDecimal]", CommutativeGroupTests[BigDecimal].commutativeGroup)
     checkAll("CommutativeGroup[BigDecimal]", SerializableTests.serializable(CommutativeGroup[BigDecimal]))
diff --git a/kernel/src/main/scala/cats/kernel/instances/BigDecimalInstances.scala b/kernel/src/main/scala/cats/kernel/instances/BigDecimalInstances.scala
index 8406336d2b..439c59ad92 100644
--- a/kernel/src/main/scala/cats/kernel/instances/BigDecimalInstances.scala
+++ b/kernel/src/main/scala/cats/kernel/instances/BigDecimalInstances.scala
@@ -8,11 +8,20 @@ trait BigDecimalInstances {
     new BigDecimalGroup
 }
 
+/**
+ * Note that combining, removing, and inverting `BigDecimal` values will use unlimited precision
+ * operations.
+ *
+ * This matches the behavior of Scala 2.12 and earlier versions, but not Scala 2.13, which means
+ * that `+` and `|+|` (or `sum` and `combineAll`) may not agree if you are working with values with
+ * limited-precision `MathContext`s.
+ */
 class BigDecimalGroup extends CommutativeGroup[BigDecimal] {
   val empty: BigDecimal = BigDecimal(0)
-  def combine(x: BigDecimal, y: BigDecimal): BigDecimal = x + y
-  def inverse(x: BigDecimal): BigDecimal = -x
-  override def remove(x: BigDecimal, y: BigDecimal): BigDecimal = x - y
+  def combine(x: BigDecimal, y: BigDecimal): BigDecimal = new BigDecimal(x.bigDecimal.add(y.bigDecimal), x.mc)
+  def inverse(x: BigDecimal): BigDecimal = new BigDecimal(x.bigDecimal.negate(), x.mc)
+  override def remove(x: BigDecimal, y: BigDecimal): BigDecimal =
+    new BigDecimal(x.bigDecimal.subtract(y.bigDecimal), x.mc)
 }
 
 class BigDecimalOrder extends Order[BigDecimal] with Hash[BigDecimal] {