diff --git a/ruma-common/CHANGELOG.md b/ruma-common/CHANGELOG.md
index def250f5..fca94afe 100644
--- a/ruma-common/CHANGELOG.md
+++ b/ruma-common/CHANGELOG.md
@@ -3,6 +3,7 @@
 Breaking changes:
 
 * Update set of conversion trait implementations for enums
+* Replace `BTreeSet` by `IndexSet` in `push::Ruleset`.
 * … (there's a lot more, but this changelog was not kept up to date; PRs to
   improve it are welcome)
 
diff --git a/ruma-common/Cargo.toml b/ruma-common/Cargo.toml
index b87c7aa9..7d5c876f 100644
--- a/ruma-common/Cargo.toml
+++ b/ruma-common/Cargo.toml
@@ -17,6 +17,7 @@ ruma-identifiers = { version = "=0.18.0-alpha.1", path = "../ruma-identifiers" }
 ruma-serde = { version = "0.3.0", path = "../ruma-serde" }
 serde = { version = "1.0.118", features = ["derive"] }
 serde_json = { version = "1.0.60", features = ["raw_value"] }
+indexmap = { version = "1.6.2", features = ["serde-1"] }
 
 [dev-dependencies]
 matches = "0.1.8"
diff --git a/ruma-common/src/push.rs b/ruma-common/src/push.rs
index 92200a7e..4b266b20 100644
--- a/ruma-common/src/push.rs
+++ b/ruma-common/src/push.rs
@@ -6,13 +6,13 @@
 //!
 //! Push rules are grouped in `RuleSet`s, and are grouped in five kinds (for
 //! more details about the different kind of rules, see the `Ruleset` documentation,
-//! or the specification). These five kinds are:
+//! or the specification). These five kinds are, by order of priority:
 //!
-//! - content rules
 //! - override rules
-//! - underride rules
+//! - content rules
 //! - room rules
 //! - sender rules
+//! - underride rules
 //!
 //! Each of these kind of rule has a corresponding type that is
 //! just a wrapper around another type:
@@ -34,8 +34,12 @@
 //! There is also the `AnyPushRule` type that is the most generic form of push rule, with all
 //! the possible fields.
 
-use std::collections::btree_set::{BTreeSet, IntoIter as BTreeSetIter};
+use std::hash::{Hash, Hasher};
 
+use indexmap::{
+    set::{IndexSet, IntoIter as IndexSetIter},
+    Equivalent,
+};
 use ruma_serde::StringEnum;
 use serde::{Deserialize, Serialize};
 
@@ -58,24 +62,24 @@ pub use self::{
 #[cfg_attr(not(feature = "unstable-exhaustive-types"), non_exhaustive)]
 pub struct Ruleset {
     /// These rules configure behavior for (unencrypted) messages that match certain patterns.
-    pub content: BTreeSet<ContentPushRule>,
+    pub content: IndexSet<ContentPushRule>,
 
     /// These user-configured rules are given the highest priority.
     ///
     /// This field is named `override_` instead of `override` because the latter is a reserved
     /// keyword in Rust.
     #[serde(rename = "override")]
-    pub override_: BTreeSet<OverridePushRule>,
+    pub override_: IndexSet<OverridePushRule>,
 
     /// These rules change the behavior of all messages for a given room.
-    pub room: BTreeSet<RoomPushRule>,
+    pub room: IndexSet<RoomPushRule>,
 
     /// These rules configure notification behavior for messages from a specific Matrix user ID.
-    pub sender: BTreeSet<SenderPushRule>,
+    pub sender: IndexSet<SenderPushRule>,
 
     /// These rules are identical to override rules, but have a lower priority than `content`,
     /// `room` and `sender` rules.
-    pub underride: BTreeSet<UnderridePushRule>,
+    pub underride: IndexSet<UnderridePushRule>,
 }
 
 impl Ruleset {
@@ -97,11 +101,11 @@ impl Ruleset {
 /// Iterator type for `Ruleset`
 #[derive(Debug)]
 pub struct RulesetIter {
-    content: BTreeSetIter<ContentPushRule>,
-    override_: BTreeSetIter<OverridePushRule>,
-    room: BTreeSetIter<RoomPushRule>,
-    sender: BTreeSetIter<SenderPushRule>,
-    underride: BTreeSetIter<UnderridePushRule>,
+    content: IndexSetIter<ContentPushRule>,
+    override_: IndexSetIter<OverridePushRule>,
+    room: IndexSetIter<RoomPushRule>,
+    sender: IndexSetIter<SenderPushRule>,
+    underride: IndexSetIter<UnderridePushRule>,
 }
 
 impl Iterator for RulesetIter {
@@ -180,17 +184,11 @@ macro_rules! rulekind {
         }
 
         // The following trait are needed to be able to make
-        // a BTreeSet of the new type
+        // an IndexSet of the new type
 
-        impl Ord for $name {
-            fn cmp(&self, other: &Self) -> core::cmp::Ordering {
-                self.0.rule_id.cmp(&other.0.rule_id)
-            }
-        }
-
-        impl PartialOrd for $name {
-            fn partial_cmp(&self, other: &Self) -> Option<core::cmp::Ordering> {
-                Some(self.cmp(other))
+        impl Hash for $name {
+            fn hash<H: Hasher>(&self, state: &mut H) {
+                self.0.rule_id.hash(state);
             }
         }
 
@@ -201,6 +199,12 @@ macro_rules! rulekind {
         }
 
         impl Eq for $name {}
+
+        impl Equivalent<$name> for str {
+            fn equivalent(&self, key: &$name) -> bool {
+                self == key.0.rule_id
+            }
+        }
     };
 }
 
diff --git a/ruma-common/src/push/predefined.rs b/ruma-common/src/push/predefined.rs
index 9628642c..d72855a1 100644
--- a/ruma-common/src/push/predefined.rs
+++ b/ruma-common/src/push/predefined.rs
@@ -1,7 +1,7 @@
 ///! Constructors for [predefined push rules].
 ///!
 ///! [predefined push rules]: https://matrix.org/docs/spec/client_server/r0.6.1#predefined-rules
-use maplit::btreeset;
+use indexmap::indexset;
 use ruma_identifiers::UserId;
 
 use super::{
@@ -20,9 +20,9 @@ impl Ruleset {
     ///   user's ID (for instance those to send notifications when they are mentioned).
     pub fn server_default(user_id: &UserId) -> Self {
         Self {
-            content: btreeset![ContentPushRule::contains_user_name(user_id)],
+            content: indexset![ContentPushRule::contains_user_name(user_id)],
             #[cfg(feature = "unstable-pre-spec")]
-            override_: btreeset![
+            override_: indexset![
                 OverridePushRule::master(),
                 OverridePushRule::suppress_notices(),
                 OverridePushRule::invite_for_me(user_id),
@@ -33,7 +33,7 @@ impl Ruleset {
                 OverridePushRule::reaction(),
             ],
             #[cfg(not(feature = "unstable-pre-spec"))]
-            override_: btreeset![
+            override_: indexset![
                 OverridePushRule::master(),
                 OverridePushRule::suppress_notices(),
                 OverridePushRule::invite_for_me(user_id),
@@ -42,7 +42,7 @@ impl Ruleset {
                 OverridePushRule::tombstone(),
                 OverridePushRule::roomnotif(),
             ],
-            underride: btreeset![
+            underride: indexset![
                 UnderridePushRule::call(),
                 UnderridePushRule::encrypted_room_one_to_one(),
                 UnderridePushRule::room_one_to_one(),