diff --git a/packages/tendermint-rpc/src/legacy/adaptors/index.ts b/packages/tendermint-rpc/src/legacy/adaptors/index.ts
index 51223aba6f..7097e36a8a 100644
--- a/packages/tendermint-rpc/src/legacy/adaptors/index.ts
+++ b/packages/tendermint-rpc/src/legacy/adaptors/index.ts
@@ -28,23 +28,15 @@ export const adaptor33 = v0_33;
  */
 export const adaptor34 = v0_33; // With this alias we can swap out the implementation without affecting caller code.
 
-const hashes = {
-  v0_34: [
-    "ca2c9df", // v0.34.0-rc6
-    "182fa32", // v0.34.0
-  ],
-};
-
 /**
  * Returns an Adaptor implementation for a given tendermint version.
  * Throws when version is not supported.
  *
  * @param version full Tendermint version string, e.g. "0.20.1"
  */
-export function adaptorForVersion(version: string): Adaptor {
-  if (version.startsWith("0.33.") || version.startsWith("0.34.") || hashes.v0_34.includes(version)) {
-    return v0_33;
-  } else {
-    throw new Error(`Unsupported tendermint version: ${version}`);
-  }
+export function adaptorForVersion(_version: string): Adaptor {
+  // Note: In some cases, Tendermint 0.34 returns an empty version value.
+  // This supports 0.33 and 0.34 now, no matter which version you provide.
+  // Very soon this function becomes obsolete (https://github.com/cosmos/cosmjs/issues/789).
+  return v0_33;
 }
diff --git a/packages/tendermint-rpc/src/legacy/client.spec.ts b/packages/tendermint-rpc/src/legacy/client.spec.ts
index a3c290a57a..eda05c4a22 100644
--- a/packages/tendermint-rpc/src/legacy/client.spec.ts
+++ b/packages/tendermint-rpc/src/legacy/client.spec.ts
@@ -167,7 +167,7 @@ function defaultTestSuite(rpcFactory: () => RpcClient, adaptor: Adaptor, expecte
       const status = await client.status();
 
       // node info
-      expect(status.nodeInfo.version).toEqual(expected.version);
+      expect(status.nodeInfo.version).toMatch(expected.version);
       expect(status.nodeInfo.protocolVersion).toEqual({
         p2p: expected.p2pVersion,
         block: expected.blockVersion,
diff --git a/packages/tendermint-rpc/src/tendermint34/adaptor.ts b/packages/tendermint-rpc/src/tendermint34/adaptor.ts
index 7248942d63..44c0691756 100644
--- a/packages/tendermint-rpc/src/tendermint34/adaptor.ts
+++ b/packages/tendermint-rpc/src/tendermint34/adaptor.ts
@@ -23,6 +23,7 @@ export interface Params {
   readonly encodeBlock: (req: requests.BlockRequest) => JsonRpcRequest;
   readonly encodeBlockchain: (req: requests.BlockchainRequest) => JsonRpcRequest;
   readonly encodeBlockResults: (req: requests.BlockResultsRequest) => JsonRpcRequest;
+  readonly encodeBlockSearch: (req: requests.BlockSearchRequest) => JsonRpcRequest;
   readonly encodeBroadcastTx: (req: requests.BroadcastTxRequest) => JsonRpcRequest;
   readonly encodeCommit: (req: requests.CommitRequest) => JsonRpcRequest;
   readonly encodeGenesis: (req: requests.GenesisRequest) => JsonRpcRequest;
@@ -39,6 +40,7 @@ export interface Responses {
   readonly decodeAbciQuery: (response: JsonRpcSuccessResponse) => responses.AbciQueryResponse;
   readonly decodeBlock: (response: JsonRpcSuccessResponse) => responses.BlockResponse;
   readonly decodeBlockResults: (response: JsonRpcSuccessResponse) => responses.BlockResultsResponse;
+  readonly decodeBlockSearch: (response: JsonRpcSuccessResponse) => responses.BlockSearchResponse;
   readonly decodeBlockchain: (response: JsonRpcSuccessResponse) => responses.BlockchainResponse;
   readonly decodeBroadcastTxSync: (response: JsonRpcSuccessResponse) => responses.BroadcastTxSyncResponse;
   readonly decodeBroadcastTxAsync: (response: JsonRpcSuccessResponse) => responses.BroadcastTxAsyncResponse;
diff --git a/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/requests.ts b/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/requests.ts
index 54436f7a07..1dc11c4c7b 100644
--- a/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/requests.ts
+++ b/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/requests.ts
@@ -30,6 +30,21 @@ function encodeBlockchainRequestParams(param: requests.BlockchainRequestParams):
   };
 }
 
+interface RpcBlockSearchParams {
+  readonly query: string;
+  readonly page?: string;
+  readonly per_page?: string;
+  readonly order_by?: string;
+}
+function encodeBlockSearchParams(params: requests.BlockSearchParams): RpcBlockSearchParams {
+  return {
+    query: params.query,
+    page: may(Integer.encode, params.page),
+    per_page: may(Integer.encode, params.per_page),
+    order_by: params.order_by,
+  };
+}
+
 interface RpcAbciQueryParams {
   readonly path: string;
   /** hex encoded */
@@ -118,6 +133,10 @@ export class Params {
     return createJsonRpcRequest(req.method, encodeHeightParam(req.params));
   }
 
+  public static encodeBlockSearch(req: requests.BlockSearchRequest): JsonRpcRequest {
+    return createJsonRpcRequest(req.method, encodeBlockSearchParams(req.params));
+  }
+
   public static encodeBroadcastTx(req: requests.BroadcastTxRequest): JsonRpcRequest {
     return createJsonRpcRequest(req.method, encodeBroadcastTxParams(req.params));
   }
diff --git a/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/responses.ts b/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/responses.ts
index 5386c7e19c..1260b8058d 100644
--- a/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/responses.ts
+++ b/packages/tendermint-rpc/src/tendermint34/adaptors/v0-34/responses.ts
@@ -284,10 +284,10 @@ interface RpcBlockId {
 
 function decodeBlockId(data: RpcBlockId): responses.BlockId {
   return {
-    hash: fromHex(assertNotEmpty(data.hash)),
+    hash: fromHex(data.hash),
     parts: {
-      total: assertNotEmpty(data.parts.total),
-      hash: fromHex(assertNotEmpty(data.parts.hash)),
+      total: data.parts.total,
+      hash: fromHex(data.parts.hash),
     },
   };
 }
@@ -349,7 +349,7 @@ function decodeHeader(data: RpcHeader): responses.Header {
     validatorsHash: fromHex(assertNotEmpty(data.validators_hash)),
     nextValidatorsHash: fromHex(assertNotEmpty(data.next_validators_hash)),
     consensusHash: fromHex(assertNotEmpty(data.consensus_hash)),
-    appHash: fromHex(assertNotEmpty(data.app_hash)),
+    appHash: fromHex(data.app_hash),
     lastResultsHash: fromHex(assertSet(data.last_results_hash)),
 
     evidenceHash: fromHex(assertSet(data.evidence_hash)),
@@ -783,6 +783,18 @@ function decodeBlockResponse(data: RpcBlockResponse): responses.BlockResponse {
   };
 }
 
+interface RpcBlockSearchResponse {
+  readonly blocks: readonly RpcBlockResponse[];
+  readonly total_count: string;
+}
+
+function decodeBlockSearch(data: RpcBlockSearchResponse): responses.BlockSearchResponse {
+  return {
+    totalCount: Integer.parse(assertNotEmpty(data.total_count)),
+    blocks: assertArray(data.blocks).map(decodeBlockResponse),
+  };
+}
+
 export class Responses {
   public static decodeAbciInfo(response: JsonRpcSuccessResponse): responses.AbciInfoResponse {
     return decodeAbciInfo(assertObject((response.result as AbciInfoResult).response));
@@ -800,6 +812,10 @@ export class Responses {
     return decodeBlockResults(response.result as RpcBlockResultsResponse);
   }
 
+  public static decodeBlockSearch(response: JsonRpcSuccessResponse): responses.BlockSearchResponse {
+    return decodeBlockSearch(response.result as RpcBlockSearchResponse);
+  }
+
   public static decodeBlockchain(response: JsonRpcSuccessResponse): responses.BlockchainResponse {
     return decodeBlockchain(response.result as RpcBlockchainResponse);
   }
diff --git a/packages/tendermint-rpc/src/tendermint34/requests.ts b/packages/tendermint-rpc/src/tendermint34/requests.ts
index d985b8e64e..75690766f0 100644
--- a/packages/tendermint-rpc/src/tendermint34/requests.ts
+++ b/packages/tendermint-rpc/src/tendermint34/requests.ts
@@ -12,6 +12,7 @@ export enum Method {
   /** Get block headers for minHeight <= height <= maxHeight. */
   Blockchain = "blockchain",
   BlockResults = "block_results",
+  BlockSearch = "block_search",
   BroadcastTxAsync = "broadcast_tx_async",
   BroadcastTxSync = "broadcast_tx_sync",
   BroadcastTxCommit = "broadcast_tx_commit",
@@ -30,6 +31,7 @@ export type Request =
   | AbciInfoRequest
   | AbciQueryRequest
   | BlockRequest
+  | BlockSearchRequest
   | BlockchainRequest
   | BlockResultsRequest
   | BroadcastTxRequest
@@ -60,6 +62,7 @@ export interface AbciQueryRequest {
   readonly method: Method.AbciQuery;
   readonly params: AbciQueryParams;
 }
+
 export interface AbciQueryParams {
   readonly path: string;
   readonly data: Uint8Array;
@@ -97,10 +100,23 @@ export interface BlockResultsRequest {
   };
 }
 
+export interface BlockSearchRequest {
+  readonly method: Method.BlockSearch;
+  readonly params: BlockSearchParams;
+}
+
+export interface BlockSearchParams {
+  readonly query: string;
+  readonly page?: number;
+  readonly per_page?: number;
+  readonly order_by?: string;
+}
+
 export interface BroadcastTxRequest {
   readonly method: Method.BroadcastTxAsync | Method.BroadcastTxSync | Method.BroadcastTxCommit;
   readonly params: BroadcastTxParams;
 }
+
 export interface BroadcastTxParams {
   readonly tx: Uint8Array;
 }
@@ -141,6 +157,7 @@ export interface TxRequest {
   readonly method: Method.Tx;
   readonly params: TxParams;
 }
+
 export interface TxParams {
   readonly hash: Uint8Array;
   readonly prove?: boolean;
diff --git a/packages/tendermint-rpc/src/tendermint34/responses.ts b/packages/tendermint-rpc/src/tendermint34/responses.ts
index ba7d39706c..b71c482612 100644
--- a/packages/tendermint-rpc/src/tendermint34/responses.ts
+++ b/packages/tendermint-rpc/src/tendermint34/responses.ts
@@ -60,6 +60,11 @@ export interface BlockResultsResponse {
   readonly endBlockEvents: readonly Event[];
 }
 
+export interface BlockSearchResponse {
+  readonly blocks: readonly BlockResponse[];
+  readonly totalCount: number;
+}
+
 export interface BlockchainResponse {
   readonly lastHeight: number;
   readonly blockMetas: readonly BlockMeta[];
diff --git a/packages/tendermint-rpc/src/tendermint34/tendermint34client.spec.ts b/packages/tendermint-rpc/src/tendermint34/tendermint34client.spec.ts
index 1f5b166612..006b33a308 100644
--- a/packages/tendermint-rpc/src/tendermint34/tendermint34client.spec.ts
+++ b/packages/tendermint-rpc/src/tendermint34/tendermint34client.spec.ts
@@ -166,7 +166,7 @@ function defaultTestSuite(rpcFactory: () => RpcClient, expected: ExpectedValues)
       const status = await client.status();
 
       // node info
-      expect(status.nodeInfo.version).toEqual(expected.version);
+      expect(status.nodeInfo.version).toMatch(expected.version);
       expect(status.nodeInfo.protocolVersion).toEqual({
         p2p: expected.p2pVersion,
         block: expected.blockVersion,
@@ -204,6 +204,69 @@ function defaultTestSuite(rpcFactory: () => RpcClient, expected: ExpectedValues)
     });
   });
 
+  describe("blockSearch", () => {
+    beforeAll(async () => {
+      if (tendermintEnabled()) {
+        const client = await Tendermint34Client.create(rpcFactory());
+
+        // eslint-disable-next-line no-inner-declarations
+        async function sendTx(): Promise<void> {
+          const tx = buildKvTx(randomString(), randomString());
+
+          const txRes = await client.broadcastTxCommit({ tx: tx });
+          expect(responses.broadcastTxCommitSuccess(txRes)).toEqual(true);
+          expect(txRes.height).toBeTruthy();
+          expect(txRes.hash.length).not.toEqual(0);
+        }
+
+        // send 3 txs
+        await sendTx();
+        await sendTx();
+        await sendTx();
+
+        client.disconnect();
+
+        await tendermintSearchIndexUpdated();
+      }
+    });
+
+    it("can paginate over blockSearch results", async () => {
+      pendingWithoutTendermint();
+      const client = await Tendermint34Client.create(rpcFactory());
+
+      const query = buildQuery({ raw: "block.height >= 1 AND block.height <= 3" });
+
+      // expect one page of results
+      const s1 = await client.blockSearch({ query: query, page: 1, per_page: 2 });
+      expect(s1.totalCount).toEqual(3);
+      expect(s1.blocks.length).toEqual(2);
+
+      // second page
+      const s2 = await client.blockSearch({ query: query, page: 2, per_page: 2 });
+      expect(s2.totalCount).toEqual(3);
+      expect(s2.blocks.length).toEqual(1);
+
+      client.disconnect();
+    });
+
+    it("can get all search results in one call", async () => {
+      pendingWithoutTendermint();
+      const client = await Tendermint34Client.create(rpcFactory());
+
+      const query = buildQuery({ raw: "block.height >= 1 AND block.height <= 3" });
+
+      const sall = await client.blockSearchAll({ query: query, per_page: 2 });
+      expect(sall.totalCount).toEqual(3);
+      expect(sall.blocks.length).toEqual(3);
+      // make sure there are in order from lowest to highest height
+      const [b1, b2, b3] = sall.blocks;
+      expect(b2.block.header.height).toEqual(b1.block.header.height + 1);
+      expect(b3.block.header.height).toEqual(b2.block.header.height + 1);
+
+      client.disconnect();
+    });
+  });
+
   describe("blockchain", () => {
     it("returns latest in descending order by default", async () => {
       pendingWithoutTendermint();
diff --git a/packages/tendermint-rpc/src/tendermint34/tendermint34client.ts b/packages/tendermint-rpc/src/tendermint34/tendermint34client.ts
index 42d20c4a7e..f528c2dd1f 100644
--- a/packages/tendermint-rpc/src/tendermint34/tendermint34client.ts
+++ b/packages/tendermint-rpc/src/tendermint34/tendermint34client.ts
@@ -98,6 +98,53 @@ export class Tendermint34Client {
     return this.doCall(query, this.p.encodeBlockResults, this.r.decodeBlockResults);
   }
 
+  /**
+   * Search for events that are in a block.
+   *
+   * NOTE
+   * This method will error on any node that is running a Tendermint version lower than 0.34.9.
+   *
+   * @see https://docs.tendermint.com/master/rpc/#/Info/block_search
+   */
+  public async blockSearch(params: requests.BlockSearchParams): Promise<responses.BlockSearchResponse> {
+    const query: requests.BlockSearchRequest = { params: params, method: requests.Method.BlockSearch };
+    const resp = await this.doCall(query, this.p.encodeBlockSearch, this.r.decodeBlockSearch);
+    return {
+      ...resp,
+      // make sure we sort by height, as tendermint may be sorting by string value of the height
+      blocks: [...resp.blocks].sort((a, b) => a.block.header.height - b.block.header.height),
+    };
+  }
+
+  // this should paginate through all blockSearch options to ensure it returns all results.
+  // starts with page 1 or whatever was provided (eg. to start on page 7)
+  //
+  // NOTE
+  // This method will error on any node that is running a Tendermint version lower than 0.34.9.
+  public async blockSearchAll(params: requests.BlockSearchParams): Promise<responses.BlockSearchResponse> {
+    let page = params.page || 1;
+    const blocks: responses.BlockResponse[] = [];
+    let done = false;
+
+    while (!done) {
+      const resp = await this.blockSearch({ ...params, page: page });
+      blocks.push(...resp.blocks);
+      if (blocks.length < resp.totalCount) {
+        page++;
+      } else {
+        done = true;
+      }
+    }
+    // make sure we sort by height, as tendermint may be sorting by string value of the height
+    // and the earlier items may be in a higher page than the later items
+    blocks.sort((a, b) => a.block.header.height - b.block.header.height);
+
+    return {
+      totalCount: blocks.length,
+      blocks: blocks,
+    };
+  }
+
   /**
    * Queries block headers filtered by minHeight <= height <= maxHeight.
    *
diff --git a/packages/tendermint-rpc/src/testutil.spec.ts b/packages/tendermint-rpc/src/testutil.spec.ts
index c7315bf5cc..353dd26fe3 100644
--- a/packages/tendermint-rpc/src/testutil.spec.ts
+++ b/packages/tendermint-rpc/src/testutil.spec.ts
@@ -1,9 +1,12 @@
 import { toAscii } from "@cosmjs/encoding";
 import { sleep } from "@cosmjs/utils";
 
+export const chainIdMatcher = /^[-a-zA-Z0-9]{3,30}$/;
+export const anyMatcher = /^.*$/; // Any string, including empty. Does not do more than a type check.
+
 export interface ExpectedValues {
   /** The Tendermint version as reported by Tendermint itself */
-  readonly version: string;
+  readonly version: string | RegExp;
   readonly appCreator: string;
   readonly p2pVersion: number;
   readonly blockVersion: number;
@@ -49,7 +52,7 @@ export const tendermintInstances: readonly TendermintInstance[] = [
     version: "0.34.x",
     blockTime: 500,
     expected: {
-      version: "182fa32", // srsly?
+      version: anyMatcher,
       appCreator: "Cosmoshi Netowoko",
       p2pVersion: 8,
       blockVersion: 11,
@@ -60,8 +63,6 @@ export const tendermintInstances: readonly TendermintInstance[] = [
 
 export const defaultInstance: TendermintInstance = tendermintInstances[0];
 
-export const chainIdMatcher = /^[-a-zA-Z0-9]{3,30}$/;
-
 export function tendermintEnabled(): boolean {
   return !!process.env.TENDERMINT_ENABLED;
 }
diff --git a/scripts/tendermint/all_start.sh b/scripts/tendermint/all_start.sh
index bbe27ca1d0..37a87fa868 100755
--- a/scripts/tendermint/all_start.sh
+++ b/scripts/tendermint/all_start.sh
@@ -5,7 +5,7 @@ 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]=v0.33.8
-TM_VERSIONS[34]=v0.34.0
+TM_VERSIONS[34]=v0.34.10
 
 SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
 
diff --git a/scripts/tendermint/all_stop.sh b/scripts/tendermint/all_stop.sh
index a2ccd3e28b..e77084df96 100755
--- a/scripts/tendermint/all_stop.sh
+++ b/scripts/tendermint/all_stop.sh
@@ -4,7 +4,7 @@ command -v shellcheck >/dev/null && shellcheck "$0"
 
 declare -a TM_VERSIONS
 TM_VERSIONS[33]=v0.33.8
-TM_VERSIONS[34]=v0.34.0
+TM_VERSIONS[34]=v0.34.10
 
 SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"