diff --git a/CHANGELOG.md b/CHANGELOG.md
index e9d3a9145d..890154ba71 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -81,6 +81,9 @@
 - @cosmjs/tendermint-rpc: Remove trivial helpers `getTxEventHeight`,
   `getHeaderEventHeight` and `getBlockEventHeight` because they don't do
   anything else than accessing an object member.
+- @cosmjs/tendermint-rpc: Add support for connecting to Tendermint RPC 0.34.
+- @cosmjs/tendermint-rpc: Make `TxEvent.index` optional and deprecate it because
+  it is not set anymore in Tendermint 0.34.
 - @cosmjs/utils: Add `assertDefined`.
 - @cosmjs/faucet: Rename binary from `cosmwasm-faucet` to `cosmos-faucet`.
 
diff --git a/packages/tendermint-rpc/src/adaptorforversion.ts b/packages/tendermint-rpc/src/adaptorforversion.ts
index eaecf1a81a..1fe1dde02d 100644
--- a/packages/tendermint-rpc/src/adaptorforversion.ts
+++ b/packages/tendermint-rpc/src/adaptorforversion.ts
@@ -11,7 +11,7 @@ import { v0_33 } from "./v0-33";
  * @param version full Tendermint version string, e.g. "0.20.1"
  */
 export function adaptorForVersion(version: string): Adaptor {
-  if (version.startsWith("0.33.")) {
+  if (version.startsWith("0.33.") || version.startsWith("0.34.")) {
     return v0_33;
   } else {
     throw new Error(`Unsupported tendermint version: ${version}`);
diff --git a/packages/tendermint-rpc/src/client.spec.ts b/packages/tendermint-rpc/src/client.spec.ts
index 13bb567df5..8c1c1a37b6 100644
--- a/packages/tendermint-rpc/src/client.spec.ts
+++ b/packages/tendermint-rpc/src/client.spec.ts
@@ -8,7 +8,7 @@ import { Stream } from "xstream";
 import { Adaptor } from "./adaptor";
 import { adaptorForVersion } from "./adaptorforversion";
 import { Client } from "./client";
-import { tendermintInstances } from "./config.spec";
+import { ExpectedValues, tendermintInstances } from "./config.spec";
 import { buildQuery } from "./requests";
 import * as responses from "./responses";
 import { HttpClient, RpcClient, WebsocketClient } from "./rpcclients";
@@ -41,7 +41,7 @@ function randomString(): string {
     .join("");
 }
 
-function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor): void {
+function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, expected: ExpectedValues): void {
   it("can connect to tendermint with known version", async () => {
     pendingWithoutTendermint();
     const client = new Client(rpcFactory(), adaptor);
@@ -133,13 +133,25 @@ function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor): void {
       const client = new Client(rpcFactory(), adaptor);
 
       const status = await client.status();
+
+      // node info
+      expect(status.nodeInfo.protocolVersion).toEqual({
+        p2p: expected.p2pVersion,
+        block: expected.blockVersion,
+        app: expected.appVersion,
+      });
+      expect(status.nodeInfo.network).toMatch(chainIdMatcher);
       expect(status.nodeInfo.other.size).toBeGreaterThanOrEqual(2);
       expect(status.nodeInfo.other.get("tx_index")).toEqual("on");
-      expect(status.validatorInfo.pubkey).toBeTruthy();
-      expect(status.validatorInfo.votingPower).toBeGreaterThan(0);
+
+      // sync info
       expect(status.syncInfo.catchingUp).toEqual(false);
       expect(status.syncInfo.latestBlockHeight).toBeGreaterThanOrEqual(1);
 
+      // validator info
+      expect(status.validatorInfo.pubkey).toBeTruthy();
+      expect(status.validatorInfo.votingPower).toBeGreaterThan(0);
+
       client.disconnect();
     });
   });
@@ -238,8 +250,8 @@ function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor): void {
         // num_txs: jasmine.stringMatching(nonNegativeIntegerMatcher),
         header: jasmine.objectContaining({
           version: {
-            block: 10,
-            app: 1,
+            block: expected.blockVersion,
+            app: expected.appVersion,
           },
           chainId: jasmine.stringMatching(chainIdMatcher),
         }),
@@ -371,7 +383,7 @@ function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor): void {
   });
 }
 
-function websocketTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, appCreator: string): void {
+function websocketTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, expected: ExpectedValues): void {
   it("can subscribe to block header events", (done) => {
     pendingWithoutTendermint();
 
@@ -498,7 +510,6 @@ function websocketTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, appCr
     const subscription = stream.subscribe({
       next: (event) => {
         expect(event.height).toBeGreaterThan(0);
-        expect(event.index).toEqual(0);
         expect(event.result).toBeTruthy();
         expect(event.result.events.length).toBeGreaterThanOrEqual(1);
 
@@ -539,13 +550,12 @@ function websocketTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, appCr
 
     const events: responses.TxEvent[] = [];
     const client = new Client(rpcFactory(), adaptor);
-    const query = buildQuery({ tags: [{ key: "app.creator", value: appCreator }] });
+    const query = buildQuery({ tags: [{ key: "app.creator", value: expected.appCreator }] });
     const stream = client.subscribeTx(query);
     expect(stream).toBeTruthy();
     const subscription = stream.subscribe({
       next: (event) => {
         expect(event.height).toBeGreaterThan(0);
-        expect(event.index).toEqual(0);
         expect(event.result).toBeTruthy();
         expect(event.result.events.length).toBeGreaterThanOrEqual(1);
         events.push(event);
@@ -622,7 +632,7 @@ function websocketTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, appCr
   });
 }
 
-for (const { url, version, appCreator } of tendermintInstances) {
+for (const { url, version, expected } of tendermintInstances) {
   describe(`Client ${version}`, () => {
     it("can connect to a given url", async () => {
       pendingWithoutTendermint();
@@ -654,7 +664,7 @@ for (const { url, version, appCreator } of tendermintInstances) {
 
     describe("With HttpClient", () => {
       const adaptor = adaptorForVersion(version);
-      defaultTestSuite(() => new HttpClient(url), adaptor);
+      defaultTestSuite(() => new HttpClient(url), adaptor, expected);
     });
 
     describe("With WebsocketClient", () => {
@@ -662,8 +672,8 @@ for (const { url, version, appCreator } of tendermintInstances) {
       const onError = process.env.TENDERMINT_ENABLED ? console.error : () => 0;
       const factory = (): WebsocketClient => new WebsocketClient(url, onError);
       const adaptor = adaptorForVersion(version);
-      defaultTestSuite(factory, adaptor);
-      websocketTestSuite(factory, adaptor, appCreator);
+      defaultTestSuite(factory, adaptor, expected);
+      websocketTestSuite(factory, adaptor, expected);
     });
   });
 }
diff --git a/packages/tendermint-rpc/src/config.spec.ts b/packages/tendermint-rpc/src/config.spec.ts
index ba8c4bbf3e..2810d856ba 100644
--- a/packages/tendermint-rpc/src/config.spec.ts
+++ b/packages/tendermint-rpc/src/config.spec.ts
@@ -1,7 +1,17 @@
+export interface ExpectedValues {
+  readonly appCreator: string;
+  readonly p2pVersion: number;
+  readonly blockVersion: number;
+  readonly appVersion: number;
+}
+
 export interface TendermintInstance {
   readonly url: string;
   readonly version: string;
-  readonly appCreator: string;
+  /** rough block time in ms */
+  readonly blockTime: number;
+  /** Values we expect in the backend */
+  readonly expected: ExpectedValues;
 }
 
 /**
@@ -20,7 +30,24 @@ export const tendermintInstances: readonly TendermintInstance[] = [
   {
     url: "localhost:11133",
     version: "0.33.x",
-    appCreator: "Cosmoshi Netowoko",
+    blockTime: 1000,
+    expected: {
+      appCreator: "Cosmoshi Netowoko",
+      p2pVersion: 7,
+      blockVersion: 10,
+      appVersion: 1,
+    },
+  },
+  {
+    url: "localhost:11134",
+    version: "0.34.x",
+    blockTime: 500,
+    expected: {
+      appCreator: "Cosmoshi Netowoko",
+      p2pVersion: 8,
+      blockVersion: 11,
+      appVersion: 1,
+    },
   },
 ];
 
diff --git a/packages/tendermint-rpc/src/responses.ts b/packages/tendermint-rpc/src/responses.ts
index 92fadb4a78..c3f78a8f82 100644
--- a/packages/tendermint-rpc/src/responses.ts
+++ b/packages/tendermint-rpc/src/responses.ts
@@ -153,7 +153,8 @@ export interface TxEvent {
   readonly tx: TxBytes;
   readonly hash: TxHash;
   readonly height: number;
-  readonly index: number;
+  /** @deprecated this value is not set in Tendermint 0.34+ */
+  readonly index?: number;
   readonly result: TxData;
 }
 
diff --git a/packages/tendermint-rpc/src/rpcclients/websocketclient.spec.ts b/packages/tendermint-rpc/src/rpcclients/websocketclient.spec.ts
index 0f15cb7904..2b3f366ab5 100644
--- a/packages/tendermint-rpc/src/rpcclients/websocketclient.spec.ts
+++ b/packages/tendermint-rpc/src/rpcclients/websocketclient.spec.ts
@@ -15,7 +15,7 @@ function pendingWithoutTendermint(): void {
 }
 
 describe("WebsocketClient", () => {
-  const tendermintUrl = defaultInstance.url;
+  const { blockTime, url: tendermintUrl } = defaultInstance;
 
   it("can make a simple call", async () => {
     pendingWithoutTendermint();
@@ -48,27 +48,27 @@ describe("WebsocketClient", () => {
 
     const events: SubscriptionEvent[] = [];
 
-    const sub = headers.subscribe({
+    const subscription = headers.subscribe({
       error: done.fail,
       complete: () => done.fail("subscription should not complete"),
-      next: (evt: SubscriptionEvent) => {
-        events.push(evt);
-        expect(evt.query).toEqual(query);
+      next: (event: SubscriptionEvent) => {
+        events.push(event);
+        expect(event.query).toEqual(query);
 
         if (events.length === 2) {
           // make sure they are consequtive heights
           const height = (i: number): number => Integer.parse(events[i].data.value.header.height);
           expect(height(1)).toEqual(height(0) + 1);
 
-          sub.unsubscribe();
+          subscription.unsubscribe();
 
-          // wait 1.5s and check we did not get more events
+          // wait 1.5 * blockTime and check we did not get more events
           setTimeout(() => {
             expect(events.length).toEqual(2);
 
             client.disconnect();
             done();
-          }, 1500);
+          }, 1.5 * blockTime);
         }
       },
     });
@@ -110,23 +110,23 @@ describe("WebsocketClient", () => {
 
     const events: SubscriptionEvent[] = [];
 
-    const sub = headers.subscribe({
+    const subscription = headers.subscribe({
       error: done.fail,
       complete: () => done.fail("subscription should not complete"),
-      next: (evt: SubscriptionEvent) => {
-        events.push(evt);
-        expect(evt.query).toEqual(query);
+      next: (event: SubscriptionEvent) => {
+        events.push(event);
+        expect(event.query).toEqual(query);
 
         if (events.length === 2) {
-          sub.unsubscribe();
+          subscription.unsubscribe();
 
-          // wait 1.5s and check we did not get more events
+          // wait 1.5 * blockTime and check we did not get more events
           setTimeout(() => {
             expect(events.length).toEqual(2);
 
             client.disconnect();
             done();
-          }, 1500);
+          }, 1.5 * blockTime);
         }
       },
     });
@@ -148,7 +148,7 @@ describe("WebsocketClient", () => {
 
     const receivedEvents: SubscriptionEvent[] = [];
 
-    setTimeout(() => client.disconnect(), 1500);
+    setTimeout(() => client.disconnect(), blockTime);
 
     headers.subscribe({
       error: done.fail,
diff --git a/packages/tendermint-rpc/src/v0-33/responses.ts b/packages/tendermint-rpc/src/v0-33/responses.ts
index 3b17a02e99..b21960a89b 100644
--- a/packages/tendermint-rpc/src/v0-33/responses.ts
+++ b/packages/tendermint-rpc/src/v0-33/responses.ts
@@ -619,7 +619,8 @@ interface RpcTxEvent {
   readonly tx: Base64String;
   readonly result: RpcTxData;
   readonly height: IntegerString;
-  readonly index: number;
+  /** Not set since Tendermint 0.34 */
+  readonly index?: number;
 }
 
 function decodeTxEvent(data: RpcTxEvent): responses.TxEvent {
@@ -629,7 +630,7 @@ function decodeTxEvent(data: RpcTxEvent): responses.TxEvent {
     hash: hashTx(tx),
     result: decodeTxData(data.result),
     height: Integer.parse(assertNotEmpty(data.height)),
-    index: Integer.parse(assertNumber(data.index)),
+    index: may(Integer.parse, data.index),
   };
 }
 
diff --git a/packages/tendermint-rpc/types/responses.d.ts b/packages/tendermint-rpc/types/responses.d.ts
index b73f6ebc37..09221e606d 100644
--- a/packages/tendermint-rpc/types/responses.d.ts
+++ b/packages/tendermint-rpc/types/responses.d.ts
@@ -120,7 +120,8 @@ export interface TxEvent {
   readonly tx: TxBytes;
   readonly hash: TxHash;
   readonly height: number;
-  readonly index: number;
+  /** @deprecated this value is not set in Tendermint 0.34+ */
+  readonly index?: number;
   readonly result: TxData;
 }
 /** An event attribute */
diff --git a/scripts/tendermint/all_start.sh b/scripts/tendermint/all_start.sh
index cfb3e4072d..05edb2c206 100755
--- a/scripts/tendermint/all_start.sh
+++ b/scripts/tendermint/all_start.sh
@@ -4,7 +4,8 @@ command -v shellcheck > /dev/null && shellcheck "$0"
 
 # Find latest patch releases at https://hub.docker.com/r/tendermint/tendermint/tags/
 declare -a TM_VERSIONS
-TM_VERSIONS[33]=v0.33.5
+TM_VERSIONS[33]=v0.33.8
+TM_VERSIONS[34]=latest
 
 SCRIPT_DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )"
 
diff --git a/scripts/tendermint/all_stop.sh b/scripts/tendermint/all_stop.sh
index c6e735f4df..4f044db815 100755
--- a/scripts/tendermint/all_stop.sh
+++ b/scripts/tendermint/all_stop.sh
@@ -3,7 +3,8 @@ set -o errexit -o nounset -o pipefail
 command -v shellcheck > /dev/null && shellcheck "$0"
 
 declare -a TM_VERSIONS
-TM_VERSIONS[33]=v0.33.5
+TM_VERSIONS[33]=v0.33.8
+TM_VERSIONS[34]=latest
 
 SCRIPT_DIR="$( cd "$( dirname "${BASH_SOURCE[0]}" )" && pwd )"
 
diff --git a/scripts/tendermint/start.sh b/scripts/tendermint/start.sh
index a1952697cb..c863f92a12 100755
--- a/scripts/tendermint/start.sh
+++ b/scripts/tendermint/start.sh
@@ -46,6 +46,7 @@ if [ -n "${CI:-}" ]; then
   # Give process some time to come alive. No idea why this helps. Needed for CI.
   sleep 0.5
 
-  # Follow the logs in CI's background job
-  tail -f "$LOGFILE"
+  # Debug start
+  sleep 3
+  cat "$LOGFILE"
 fi