diff --git a/types/coin.go b/types/coin.go
index ca63fa32a634..c8b7c77db77d 100644
--- a/types/coin.go
+++ b/types/coin.go
@@ -390,19 +390,65 @@ func (coins Coins) SafeSub(coinsB Coins) (Coins, bool) {
 	return diff, diff.IsAnyNegative()
 }
 
-// Max returns the maximum of each denom of its inputs.
-// The inputs should be sorted. Note that the max might
-// not be equal to either of its inputs. Uses multiset
-// semantics, so unmentioned denoms are implicitly zero.
+// Max takes two valid Coins inputs and returns a valid Coins result
+// where for every denom D, AmountOf(D) of the result is the maximum
+// of AmountOf(D) of the inputs.  Note that the result might be not
+// be equal to either input. For any valid Coins a, b, and c, the
+// following are always true:
+//     a.IsAllLTE(a.Max(b))
+//     b.IsAllLTE(a.Max(b))
+//     a.IsAllLTE(c) && b.IsAllLTE(c) == a.Max(b).IsAllLTE(c)
+//     a.Add(b...).IsEqual(a.Min(b).Add(a.Max(b)...))
+//
+// E.g.
+// {1A, 3B, 2C}.Max({4A, 2B, 2C} == {4A, 3B, 2C})
+// {2A, 3B}.Max({1B, 4C}) == {2A, 3B, 4C}
+// {1A, 2B}.Max({}) == {1A, 2B}
 func (coins Coins) Max(coinsB Coins) Coins {
-	// coins + coinsB == min(coins, coinsB) + max(coins, coinsB)
-	return coins.Add(coinsB...).Sub(coins.Min(coinsB))
+	max := make([]Coin, 0)
+	indexA, indexB := 0, 0
+	for indexA < len(coins) && indexB < len(coinsB) {
+		coinA, coinB := coins[indexA], coinsB[indexB]
+		switch strings.Compare(coinA.Denom, coinB.Denom) {
+		case -1: // denom missing from coinsB
+			max = append(max, coinA)
+			indexA++
+		case 0: // same denom in both
+			maxCoin := coinA
+			if coinB.Amount.GT(maxCoin.Amount) {
+				maxCoin = coinB
+			}
+			max = append(max, maxCoin)
+			indexA++
+			indexB++
+		case 1: // denom missing from coinsA
+			max = append(max, coinB)
+			indexB++
+		}
+	}
+	for ; indexA < len(coins); indexA++ {
+		max = append(max, coins[indexA])
+	}
+	for ; indexB < len(coinsB); indexB++ {
+		max = append(max, coinsB[indexB])
+	}
+	return NewCoins(max...)
 }
 
-// Min returns the minimum of each denom of its inputs.
-// The inputs should be sorted. Note that the min might
-// not be equal to either of its inputs. Uses multiset
-// semantics, so unmentioned denoms are implicitly zero.
+// Min takes two valid Coins inputs and returns a valid Coins result
+// where for every denom D, AmountOf(D) of the result is the minimum
+// of AmountOf(D) of the inputs.  Note that the result might be not
+// be equal to either input. For any valid Coins a, b, and c, the
+// following are always true:
+//     a.Min(b).IsAllLTE(a)
+//     a.Min(b).IsAllLTE(b)
+//     c.IsAllLTE(a) && c.IsAllLTE(b) == c.IsAllLTE(a.Min(b))
+//     a.Add(b...).IsEqual(a.Min(b).Add(a.Max(b)...))
+//
+// E.g.
+// {1A, 3B, 2C}.Min({4A, 2B, 2C} == {1A, 2B, 2C})
+// {2A, 3B}.Min({1B, 4C}) == {1B}
+// {1A, 2B}.Min({3C}) == empty
 func (coins Coins) Min(coinsB Coins) Coins {
 	min := make([]Coin, 0)
 	for indexA, indexB := 0, 0; indexA < len(coins) && indexB < len(coinsB); {
diff --git a/types/coin_test.go b/types/coin_test.go
index f82b581aa691..11567bd3a5e4 100644
--- a/types/coin_test.go
+++ b/types/coin_test.go
@@ -679,8 +679,10 @@ func (s *coinTestSuite) TestMinMax() {
 	for _, tc := range cases {
 		min := tc.input1.Min(tc.input2)
 		max := tc.input1.Max(tc.input2)
+		intersect := tc.input1.Intersect(tc.input2)
 		s.Require().True(min.IsEqual(tc.min), tc.name)
 		s.Require().True(max.IsEqual(tc.max), tc.name)
+		s.Require().True(intersect.IsEqual(tc.min), tc.name)
 	}
 }