diff --git a/substrate/frame/democracy/src/tests.rs b/substrate/frame/democracy/src/tests.rs
index 4dd96d219b..9df594ed07 100644
--- a/substrate/frame/democracy/src/tests.rs
+++ b/substrate/frame/democracy/src/tests.rs
@@ -22,7 +22,7 @@ use super::*;
 use codec::Encode;
 use frame_support::{
 	assert_noop, assert_ok, parameter_types, ord_parameter_types,
-	traits::{Contains, OnInitialize, Filter},
+	traits::{SortedMembers, OnInitialize, Filter},
 	weights::Weight,
 };
 use sp_core::H256;
@@ -151,7 +151,7 @@ ord_parameter_types! {
 	pub const Six: u64 = 6;
 }
 pub struct OneToFive;
-impl Contains<u64> for OneToFive {
+impl SortedMembers<u64> for OneToFive {
 	fn sorted_members() -> Vec<u64> {
 		vec![1, 2, 3, 4, 5]
 	}
diff --git a/substrate/frame/elections-phragmen/src/lib.rs b/substrate/frame/elections-phragmen/src/lib.rs
index 6317bcebac..c7fcb4cec8 100644
--- a/substrate/frame/elections-phragmen/src/lib.rs
+++ b/substrate/frame/elections-phragmen/src/lib.rs
@@ -107,7 +107,7 @@ use frame_support::{
 	traits::{
 		ChangeMembers, Contains, ContainsLengthBound, Currency, CurrencyToVote, Get,
 		InitializeMembers, LockIdentifier, LockableCurrency, OnUnbalanced, ReservableCurrency,
-		WithdrawReasons,
+		WithdrawReasons, SortedMembers,
 	},
 	weights::Weight,
 };
@@ -1015,6 +1015,12 @@ impl<T: Config> Contains<T::AccountId> for Module<T> {
 	fn contains(who: &T::AccountId) -> bool {
 		Self::is_member(who)
 	}
+}
+
+impl<T: Config> SortedMembers<T::AccountId> for Module<T> {
+	fn contains(who: &T::AccountId) -> bool {
+		Self::is_member(who)
+	}
 
 	fn sorted_members() -> Vec<T::AccountId> {
 		Self::members_ids()
diff --git a/substrate/frame/membership/src/lib.rs b/substrate/frame/membership/src/lib.rs
index 532a235ad3..7ad7d6a543 100644
--- a/substrate/frame/membership/src/lib.rs
+++ b/substrate/frame/membership/src/lib.rs
@@ -26,7 +26,7 @@
 use sp_std::prelude::*;
 use frame_support::{
 	decl_module, decl_storage, decl_event, decl_error,
-	traits::{ChangeMembers, InitializeMembers, EnsureOrigin, Contains},
+	traits::{ChangeMembers, InitializeMembers, EnsureOrigin, Contains, SortedMembers},
 };
 use frame_system::ensure_signed;
 
@@ -267,6 +267,12 @@ impl<T: Config<I>, I: Instance> Module<T, I> {
 }
 
 impl<T: Config<I>, I: Instance> Contains<T::AccountId> for Module<T, I> {
+	fn contains(t: &T::AccountId) -> bool {
+		Self::members().binary_search(t).is_ok()
+	}
+}
+
+impl<T: Config<I>, I: Instance> SortedMembers<T::AccountId> for Module<T, I> {
 	fn sorted_members() -> Vec<T::AccountId> {
 		Self::members()
 	}
diff --git a/substrate/frame/support/src/lib.rs b/substrate/frame/support/src/lib.rs
index 13feab8ed3..92ffe0cb0c 100644
--- a/substrate/frame/support/src/lib.rs
+++ b/substrate/frame/support/src/lib.rs
@@ -459,13 +459,16 @@ macro_rules! ord_parameter_types {
 	);
 	() => ();
 	(IMPL $name:ident , $type:ty , $value:expr) => {
-		impl $crate::traits::Contains<$type> for $name {
+		impl $crate::traits::SortedMembers<$type> for $name {
 			fn contains(t: &$type) -> bool { &$value == t }
 			fn sorted_members() -> $crate::sp_std::prelude::Vec<$type> { vec![$value] }
 			fn count() -> usize { 1 }
 			#[cfg(feature = "runtime-benchmarks")]
 			fn add(_: &$type) {}
 		}
+		impl $crate::traits::Contains<$type> for $name {
+			fn contains(t: &$type) -> bool { &$value == t }
+		}
 	}
 }
 
diff --git a/substrate/frame/support/src/traits.rs b/substrate/frame/support/src/traits.rs
index 6fd40aa9ba..7288f6c0d2 100644
--- a/substrate/frame/support/src/traits.rs
+++ b/substrate/frame/support/src/traits.rs
@@ -29,7 +29,10 @@ pub use tokens::imbalance::{Imbalance, OnUnbalanced, SignedImbalance};
 pub use tokens::{ExistenceRequirement, WithdrawReasons, BalanceStatus};
 
 mod members;
-pub use members::{Contains, ContainsLengthBound, InitializeMembers, ChangeMembers};
+pub use members::{
+	Contains, ContainsLengthBound, SortedMembers, InitializeMembers, ChangeMembers, All, IsInVec,
+	AsContains,
+};
 
 mod validation;
 pub use validation::{
diff --git a/substrate/frame/support/src/traits/members.rs b/substrate/frame/support/src/traits/members.rs
index d3ce6786af..35748ca9c0 100644
--- a/substrate/frame/support/src/traits/members.rs
+++ b/substrate/frame/support/src/traits/members.rs
@@ -17,16 +17,28 @@
 
 //! Traits for dealing with the idea of membership.
 
-use sp_std::prelude::*;
+use sp_std::{prelude::*, marker::PhantomData};
 
 /// A trait for querying whether a type can be said to "contain" a value.
-pub trait Contains<T: Ord> {
+pub trait Contains<T> {
 	/// Return `true` if this "contains" the given value `t`.
-	fn contains(t: &T) -> bool { Self::sorted_members().binary_search(t).is_ok() }
+	fn contains(t: &T) -> bool;
+}
 
+/// A `Contains` implementation which always returns `true`.
+pub struct All<T>(PhantomData<T>);
+impl<T: Ord> Contains<T> for All<T> {
+	fn contains(_: &T) -> bool { true }
+}
+
+/// A trait for a set which can enumerate its members in order.
+pub trait SortedMembers<T: Ord> {
 	/// Get a vector of all members in the set, ordered.
 	fn sorted_members() -> Vec<T>;
 
+	/// Return `true` if this "contains" the given value `t`.
+	fn contains(t: &T) -> bool { Self::sorted_members().binary_search(t).is_ok() }
+
 	/// Get the number of items in the set.
 	fn count() -> usize { Self::sorted_members().len() }
 
@@ -38,6 +50,21 @@ pub trait Contains<T: Ord> {
 	fn add(_t: &T) { unimplemented!() }
 }
 
+/// Adapter struct for turning an `OrderedMembership` impl into a `Contains` impl.
+pub struct AsContains<OM>(PhantomData<(OM,)>);
+impl<T: Ord + Eq, OM: SortedMembers<T>> Contains<T> for AsContains<OM> {
+	fn contains(t: &T) -> bool { OM::contains(t) }
+}
+
+/// Trivial utility for implementing `Contains`/`OrderedMembership` with a `Vec`.
+pub struct IsInVec<T>(PhantomData<T>);
+impl<X: Eq, T: super::Get<Vec<X>>> Contains<X> for IsInVec<T> {
+	fn contains(t: &X) -> bool { T::get().contains(t) }
+}
+impl<X: Ord + PartialOrd, T: super::Get<Vec<X>>> SortedMembers<X> for IsInVec<T> {
+	fn sorted_members() -> Vec<X> { let mut r = T::get(); r.sort(); r }
+}
+
 /// A trait for querying bound for the length of an implementation of `Contains`
 pub trait ContainsLengthBound {
 	/// Minimum number of elements contained
diff --git a/substrate/frame/system/src/lib.rs b/substrate/frame/system/src/lib.rs
index d8a50f9f7a..bd6ef5eb50 100644
--- a/substrate/frame/system/src/lib.rs
+++ b/substrate/frame/system/src/lib.rs
@@ -87,7 +87,7 @@ use sp_core::{ChangesTrieConfiguration, storage::well_known_keys};
 use frame_support::{
 	Parameter, storage,
 	traits::{
-		Contains, Get, PalletInfo, OnNewAccount, OnKilledAccount, HandleLifetime,
+		SortedMembers, Get, PalletInfo, OnNewAccount, OnKilledAccount, HandleLifetime,
 		StoredMap, EnsureOrigin, OriginTrait, Filter,
 	},
 	weights::{
@@ -870,7 +870,7 @@ impl<
 pub struct EnsureSignedBy<Who, AccountId>(sp_std::marker::PhantomData<(Who, AccountId)>);
 impl<
 	O: Into<Result<RawOrigin<AccountId>, O>> + From<RawOrigin<AccountId>>,
-	Who: Contains<AccountId>,
+	Who: SortedMembers<AccountId>,
 	AccountId: PartialEq + Clone + Ord + Default,
 > EnsureOrigin<O> for EnsureSignedBy<Who, AccountId> {
 	type Success = AccountId;
diff --git a/substrate/frame/tips/src/lib.rs b/substrate/frame/tips/src/lib.rs
index 10b2b01683..b31468797c 100644
--- a/substrate/frame/tips/src/lib.rs
+++ b/substrate/frame/tips/src/lib.rs
@@ -68,7 +68,7 @@ use frame_support::traits::{
 use sp_runtime::{ Percent, RuntimeDebug, traits::{
 	Zero, AccountIdConversion, Hash, BadOrigin
 }};
-use frame_support::traits::{Contains, ContainsLengthBound, OnUnbalanced, EnsureOrigin};
+use frame_support::traits::{SortedMembers, ContainsLengthBound, OnUnbalanced, EnsureOrigin};
 use codec::{Encode, Decode};
 use frame_system::{self as system, ensure_signed};
 pub use weights::WeightInfo;
@@ -86,7 +86,7 @@ pub trait Config: frame_system::Config + pallet_treasury::Config {
 	/// Origin from which tippers must come.
 	///
 	/// `ContainsLengthBound::max_len` must be cost free (i.e. no storage read or heavy operation).
-	type Tippers: Contains<Self::AccountId> + ContainsLengthBound;
+	type Tippers: SortedMembers<Self::AccountId> + ContainsLengthBound;
 
 	/// The period for which a tip remains open after is has achieved threshold tippers.
 	type TipCountdown: Get<Self::BlockNumber>;
diff --git a/substrate/frame/tips/src/tests.rs b/substrate/frame/tips/src/tests.rs
index 9524c136aa..cb0d4e6c47 100644
--- a/substrate/frame/tips/src/tests.rs
+++ b/substrate/frame/tips/src/tests.rs
@@ -24,7 +24,7 @@ use super::*;
 use std::cell::RefCell;
 use frame_support::{
 	assert_noop, assert_ok, parameter_types,
-	weights::Weight, traits::Contains,
+	weights::Weight, traits::SortedMembers,
 	PalletId
 };
 use sp_runtime::Permill;
@@ -98,7 +98,7 @@ thread_local! {
 	static TEN_TO_FOURTEEN: RefCell<Vec<u128>> = RefCell::new(vec![10,11,12,13,14]);
 }
 pub struct TenToFourteen;
-impl Contains<u128> for TenToFourteen {
+impl SortedMembers<u128> for TenToFourteen {
 	fn sorted_members() -> Vec<u128> {
 		TEN_TO_FOURTEEN.with(|v| {
 			v.borrow().clone()