diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1768da89..f5305260 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -16,6 +16,13 @@
 - @cosmjs/sdk38: Remove `Pen` type in favour of `OfflineSigner` and remove
   `Secp256k1Pen` class in favour of `Secp256k1Wallet` which takes an
   `OfflineSigner` instead of a `SigningCallback`.
+- @cosmjs/sdk38: Rename `CosmosSdkAccount` to `BaseAccount` and export the type.
+- @cosmjs/sdk38: `BaseAccount` now uses `number | string` as the type for
+  `account_number` and `sequence`. The new helpers `uint64ToNumber` and
+  `uint64ToString` allow you to normalize the mixed input.
+- @cosmjs/sdk38: `BaseAccount` now uses `string | PubKey | null` as the type for
+  `public_key`. The new helper `normalizePubkey` allows you to normalize the
+  mixed input.
 - @cosmjs/math: Add missing integer check to `Uint64.fromNumber`. Before
   `Uint64.fromNumber(1.1)` produced some result.
 - @cosmjs/sdk38: Add `SigningCosmosClient.signAndPost` as a mid-level
diff --git a/packages/cosmwasm/src/cosmwasmclient.ts b/packages/cosmwasm/src/cosmwasmclient.ts
index f2543c97..c16a8965 100644
--- a/packages/cosmwasm/src/cosmwasmclient.ts
+++ b/packages/cosmwasm/src/cosmwasmclient.ts
@@ -6,13 +6,14 @@ import {
   BroadcastMode,
   Coin,
   CosmosSdkTx,
-  decodeBech32Pubkey,
   IndexedTx,
   LcdClient,
+  normalizePubkey,
   PostTxResult,
   PubKey,
   setupAuthExtension,
   StdTx,
+  uint64ToNumber,
 } from "@cosmjs/sdk38";
 
 import { setupWasmExtension, WasmExtension } from "./lcdapi/wasm";
@@ -233,9 +234,9 @@ export class CosmWasmClient {
       return {
         address: value.address,
         balance: value.coins,
-        pubkey: value.public_key ? decodeBech32Pubkey(value.public_key) : undefined,
-        accountNumber: value.account_number,
-        sequence: value.sequence,
+        pubkey: normalizePubkey(value.public_key) || undefined,
+        accountNumber: uint64ToNumber(value.account_number),
+        sequence: uint64ToNumber(value.sequence),
       };
     }
   }
diff --git a/packages/sdk38/src/cosmosclient.ts b/packages/sdk38/src/cosmosclient.ts
index 34ee4fe0..555afd43 100644
--- a/packages/sdk38/src/cosmosclient.ts
+++ b/packages/sdk38/src/cosmosclient.ts
@@ -3,9 +3,15 @@ import { fromBase64, fromHex, toHex } from "@cosmjs/encoding";
 import { Uint53 } from "@cosmjs/math";
 
 import { Coin } from "./coins";
-import { AuthExtension, BroadcastMode, LcdClient, setupAuthExtension } from "./lcdapi";
+import {
+  AuthExtension,
+  BroadcastMode,
+  LcdClient,
+  normalizePubkey,
+  setupAuthExtension,
+  uint64ToNumber,
+} from "./lcdapi";
 import { Log, parseLogs } from "./logs";
-import { decodeBech32Pubkey } from "./pubkey";
 import { CosmosSdkTx, PubKey, StdTx } from "./types";
 
 export interface GetSequenceResult {
@@ -234,9 +240,9 @@ export class CosmosClient {
       return {
         address: value.address,
         balance: value.coins,
-        pubkey: value.public_key ? decodeBech32Pubkey(value.public_key) : undefined,
-        accountNumber: value.account_number,
-        sequence: value.sequence,
+        pubkey: normalizePubkey(value.public_key) || undefined,
+        accountNumber: uint64ToNumber(value.account_number),
+        sequence: uint64ToNumber(value.sequence),
       };
     }
   }
diff --git a/packages/sdk38/src/encoding.ts b/packages/sdk38/src/encoding.ts
index 70ef1f23..17f8de77 100644
--- a/packages/sdk38/src/encoding.ts
+++ b/packages/sdk38/src/encoding.ts
@@ -1,6 +1,7 @@
 /* eslint-disable @typescript-eslint/naming-convention */
 import { toUtf8 } from "@cosmjs/encoding";
 
+import { uint64ToString } from "./lcdapi";
 import { Msg } from "./msgs";
 import { StdFee } from "./types";
 
@@ -41,16 +42,16 @@ export function makeSignBytes(
   fee: StdFee,
   chainId: string,
   memo: string,
-  accountNumber: number,
-  sequence: number,
+  accountNumber: number | string,
+  sequence: number | string,
 ): Uint8Array {
   const signDoc: StdSignDoc = {
-    account_number: accountNumber.toString(),
+    account_number: uint64ToString(accountNumber),
     chain_id: chainId,
     fee: fee,
     memo: memo,
     msgs: msgs,
-    sequence: sequence.toString(),
+    sequence: uint64ToString(sequence),
   };
   const sortedSignDoc = sortJson(signDoc);
   return toUtf8(JSON.stringify(sortedSignDoc));
diff --git a/packages/sdk38/src/index.ts b/packages/sdk38/src/index.ts
index 4afe6c26..05adf9ce 100644
--- a/packages/sdk38/src/index.ts
+++ b/packages/sdk38/src/index.ts
@@ -30,6 +30,7 @@ export {
   AuthExtension,
   BankBalancesResponse,
   BankExtension,
+  BaseAccount,
   BlockResponse,
   BroadcastMode,
   DistributionCommunityPoolResponse,
@@ -60,6 +61,7 @@ export {
   MintParametersResponse,
   NodeInfoResponse,
   normalizeLcdApiArray,
+  normalizePubkey,
   PostTxsResponse,
   SearchTxsResponse,
   setupAuthExtension,
@@ -78,6 +80,8 @@ export {
   StakingPoolResponse,
   SupplyExtension,
   TxsResponse,
+  uint64ToNumber,
+  uint64ToString,
 } from "./lcdapi";
 export { isMsgDelegate, isMsgSend, Msg, MsgDelegate, MsgSend } from "./msgs";
 export { decodeBech32Pubkey, encodeBech32Pubkey, encodeSecp256k1Pubkey } from "./pubkey";
diff --git a/packages/sdk38/src/lcdapi/auth.ts b/packages/sdk38/src/lcdapi/auth.ts
index 942d117b..6b316466 100644
--- a/packages/sdk38/src/lcdapi/auth.ts
+++ b/packages/sdk38/src/lcdapi/auth.ts
@@ -1,22 +1,58 @@
 /* eslint-disable @typescript-eslint/naming-convention */
 import { Coin } from "../coins";
+import { PubKey } from "../types";
 import { LcdClient } from "./lcdclient";
 
-export interface CosmosSdkAccount {
+/**
+ * A Cosmos SDK base account.
+ *
+ * This type describes the base account representation as returned
+ * by the Cosmos SDK 0.37–0.39 LCD API.
+ *
+ * @see https://docs.cosmos.network/master/modules/auth/02_state.html#base-account
+ */
+export interface BaseAccount {
   /** Bech32 account address */
   readonly address: string;
   readonly coins: readonly Coin[];
-  /** Bech32 encoded pubkey */
-  readonly public_key: string;
-  readonly account_number: number;
-  readonly sequence: number;
+  /**
+   * The public key of the account. This is not available on-chain as long as the account
+   * did not send a transaction.
+   *
+   * This was a type/value object in Cosmos SDK 0.37, changed to bech32 in Cosmos SDK 0.38 ([1])
+   * and changed back to type/value object in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly public_key: string | PubKey | null;
+  /**
+   * The account number assigned by the blockchain.
+   *
+   * This was string encoded in Cosmos SDK 0.37, changed to number in Cosmos SDK 0.38 ([1])
+   * and changed back to string in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly account_number: number | string;
+  /**
+   * The sequence number for replay protection.
+   *
+   * This was string encoded in Cosmos SDK 0.37, changed to number in Cosmos SDK 0.38 ([1])
+   * and changed back to string in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly sequence: number | string;
 }
 
 export interface AuthAccountsResponse {
   readonly height: string;
   readonly result: {
     readonly type: "cosmos-sdk/Account";
-    readonly value: CosmosSdkAccount;
+    readonly value: BaseAccount;
   };
 }
 
diff --git a/packages/sdk38/src/lcdapi/index.ts b/packages/sdk38/src/lcdapi/index.ts
index 5a3fc580..db3bdb73 100644
--- a/packages/sdk38/src/lcdapi/index.ts
+++ b/packages/sdk38/src/lcdapi/index.ts
@@ -2,7 +2,7 @@
 // Standard modules (see tracking issue https://github.com/CosmWasm/cosmjs/issues/276)
 //
 
-export { AuthExtension, AuthAccountsResponse, setupAuthExtension } from "./auth";
+export { AuthExtension, AuthAccountsResponse, BaseAccount, setupAuthExtension } from "./auth";
 export { BankBalancesResponse, BankExtension, setupBankExtension } from "./bank";
 export {
   DistributionCommunityPoolResponse,
@@ -77,3 +77,8 @@ export {
   TxsResponse,
 } from "./base";
 export { LcdApiArray, LcdClient, normalizeLcdApiArray } from "./lcdclient";
+
+//
+// Utils for interacting with the client/API
+//
+export { normalizePubkey, uint64ToNumber, uint64ToString } from "./utils";
diff --git a/packages/sdk38/src/lcdapi/utils.spec.ts b/packages/sdk38/src/lcdapi/utils.spec.ts
new file mode 100644
index 00000000..ace1c60e
--- /dev/null
+++ b/packages/sdk38/src/lcdapi/utils.spec.ts
@@ -0,0 +1,94 @@
+import { PubKey } from "../types";
+import { normalizePubkey, uint64ToNumber, uint64ToString } from "./utils";
+
+describe("utils", () => {
+  describe("uint64ToNumber", () => {
+    it("works for numeric inputs", () => {
+      expect(uint64ToNumber(0)).toEqual(0);
+      expect(uint64ToNumber(1)).toEqual(1);
+      expect(uint64ToNumber(Number.MAX_SAFE_INTEGER)).toEqual(Number.MAX_SAFE_INTEGER);
+    });
+
+    it("works for string inputs", () => {
+      expect(uint64ToNumber("0")).toEqual(0);
+      expect(uint64ToNumber("1")).toEqual(1);
+      expect(uint64ToNumber("9007199254740991")).toEqual(Number.MAX_SAFE_INTEGER);
+    });
+
+    it("throws for invalid numbers", () => {
+      expect(() => uint64ToNumber(NaN)).toThrow();
+      expect(() => uint64ToNumber(1.1)).toThrow();
+      expect(() => uint64ToNumber(-1)).toThrow();
+      expect(() => uint64ToNumber(Number.MAX_SAFE_INTEGER + 1)).toThrow();
+    });
+
+    it("throws for invalid strings", () => {
+      expect(() => uint64ToNumber("")).toThrow();
+      expect(() => uint64ToNumber("0x22")).toThrow();
+      expect(() => uint64ToNumber("-1")).toThrow();
+      expect(() => uint64ToNumber("1.1")).toThrow();
+      expect(() => uint64ToNumber("9007199254740992")).toThrow();
+    });
+  });
+
+  describe("uint64ToString", () => {
+    it("works for numeric inputs", () => {
+      expect(uint64ToString(0)).toEqual("0");
+      expect(uint64ToString(1)).toEqual("1");
+      expect(uint64ToString(Number.MAX_SAFE_INTEGER)).toEqual("9007199254740991");
+    });
+
+    it("works for string inputs", () => {
+      expect(uint64ToString("0")).toEqual("0");
+      expect(uint64ToString("1")).toEqual("1");
+      expect(uint64ToString("9007199254740991")).toEqual("9007199254740991");
+    });
+
+    it("works for large string values", () => {
+      // for the string -> string version, the full uint64 range is supported
+      expect(uint64ToString("9007199254740992")).toEqual("9007199254740992");
+      expect(uint64ToString("18446744073709551615")).toEqual("18446744073709551615");
+    });
+
+    it("throws for invalid numbers", () => {
+      expect(() => uint64ToString(NaN)).toThrow();
+      expect(() => uint64ToString(1.1)).toThrow();
+      expect(() => uint64ToString(-1)).toThrow();
+      expect(() => uint64ToString(Number.MAX_SAFE_INTEGER + 1)).toThrow();
+    });
+
+    it("throws for invalid strings", () => {
+      expect(() => uint64ToString("")).toThrow();
+      expect(() => uint64ToString("0x22")).toThrow();
+      expect(() => uint64ToString("-1")).toThrow();
+      expect(() => uint64ToString("1.1")).toThrow();
+      expect(() => uint64ToString("18446744073709551616")).toThrow();
+    });
+  });
+
+  describe("normalizePubkey", () => {
+    it("interprets empty bech32 string as unset", () => {
+      expect(normalizePubkey("")).toBeNull();
+    });
+
+    it("decodes bech32 pubkey", () => {
+      const input = "cosmospub1addwnpepqd8sgxq7aw348ydctp3n5ajufgxp395hksxjzc6565yfp56scupfqhlgyg5";
+      expect(normalizePubkey(input)).toEqual({
+        type: "tendermint/PubKeySecp256k1",
+        value: "A08EGB7ro1ORuFhjOnZcSgwYlpe0DSFjVNUIkNNQxwKQ",
+      });
+    });
+
+    it("interprets null as unset", () => {
+      expect(normalizePubkey(null)).toBeNull();
+    });
+
+    it("passes PubKey unchanged", () => {
+      const original: PubKey = {
+        type: "tendermint/PubKeySecp256k1",
+        value: "A08EGB7ro1ORuFhjOnZcSgwYlpe0DSFjVNUIkNNQxwKQ",
+      };
+      expect(original).toEqual(original);
+    });
+  });
+});
diff --git a/packages/sdk38/src/lcdapi/utils.ts b/packages/sdk38/src/lcdapi/utils.ts
new file mode 100644
index 00000000..5f797746
--- /dev/null
+++ b/packages/sdk38/src/lcdapi/utils.ts
@@ -0,0 +1,38 @@
+import { Uint64 } from "@cosmjs/math";
+
+import { decodeBech32Pubkey } from "../pubkey";
+import { PubKey } from "../types";
+
+/**
+ * Converts an integer expressed as number or string to a number.
+ * Throws if input is not a valid uint64 or if the value exceeds MAX_SAFE_INTEGER.
+ *
+ * This is needed for supporting Comsos SDK 0.37/0.38/0.39 with one client.
+ */
+export function uint64ToNumber(input: number | string): number {
+  const value = typeof input === "number" ? Uint64.fromNumber(input) : Uint64.fromString(input);
+  return value.toNumber();
+}
+
+/**
+ * Converts an integer expressed as number or string to a string.
+ * Throws if input is not a valid uint64.
+ *
+ * This is needed for supporting Comsos SDK 0.37/0.38/0.39 with one client.
+ */
+export function uint64ToString(input: number | string): string {
+  const value = typeof input === "number" ? Uint64.fromNumber(input) : Uint64.fromString(input);
+  return value.toString();
+}
+
+/**
+ * Normalizes a pubkey as in `BaseAccount.public_key` to allow supporting
+ * Comsos SDK 0.37–0.39.
+ *
+ * Returns null when unset.
+ */
+export function normalizePubkey(input: string | PubKey | null): PubKey | null {
+  if (!input) return null;
+  if (typeof input === "string") return decodeBech32Pubkey(input);
+  return input;
+}
diff --git a/packages/sdk38/types/encoding.d.ts b/packages/sdk38/types/encoding.d.ts
index 6eece8ca..35885e4d 100644
--- a/packages/sdk38/types/encoding.d.ts
+++ b/packages/sdk38/types/encoding.d.ts
@@ -5,6 +5,6 @@ export declare function makeSignBytes(
   fee: StdFee,
   chainId: string,
   memo: string,
-  accountNumber: number,
-  sequence: number,
+  accountNumber: number | string,
+  sequence: number | string,
 ): Uint8Array;
diff --git a/packages/sdk38/types/index.d.ts b/packages/sdk38/types/index.d.ts
index d84be9f2..b136e0d0 100644
--- a/packages/sdk38/types/index.d.ts
+++ b/packages/sdk38/types/index.d.ts
@@ -28,6 +28,7 @@ export {
   AuthExtension,
   BankBalancesResponse,
   BankExtension,
+  BaseAccount,
   BlockResponse,
   BroadcastMode,
   DistributionCommunityPoolResponse,
@@ -58,6 +59,7 @@ export {
   MintParametersResponse,
   NodeInfoResponse,
   normalizeLcdApiArray,
+  normalizePubkey,
   PostTxsResponse,
   SearchTxsResponse,
   setupAuthExtension,
@@ -76,6 +78,8 @@ export {
   StakingPoolResponse,
   SupplyExtension,
   TxsResponse,
+  uint64ToNumber,
+  uint64ToString,
 } from "./lcdapi";
 export { isMsgDelegate, isMsgSend, Msg, MsgDelegate, MsgSend } from "./msgs";
 export { decodeBech32Pubkey, encodeBech32Pubkey, encodeSecp256k1Pubkey } from "./pubkey";
diff --git a/packages/sdk38/types/lcdapi/auth.d.ts b/packages/sdk38/types/lcdapi/auth.d.ts
index 95f404d3..e20b7102 100644
--- a/packages/sdk38/types/lcdapi/auth.d.ts
+++ b/packages/sdk38/types/lcdapi/auth.d.ts
@@ -1,19 +1,55 @@
 import { Coin } from "../coins";
+import { PubKey } from "../types";
 import { LcdClient } from "./lcdclient";
-export interface CosmosSdkAccount {
+/**
+ * A Cosmos SDK base account.
+ *
+ * This type describes the base account representation as returned
+ * by the Cosmos SDK 0.37–0.39 LCD API.
+ *
+ * @see https://docs.cosmos.network/master/modules/auth/02_state.html#base-account
+ */
+export interface BaseAccount {
   /** Bech32 account address */
   readonly address: string;
   readonly coins: readonly Coin[];
-  /** Bech32 encoded pubkey */
-  readonly public_key: string;
-  readonly account_number: number;
-  readonly sequence: number;
+  /**
+   * The public key of the account. This is not available on-chain as long as the account
+   * did not send a transaction.
+   *
+   * This was a type/value object in Cosmos SDK 0.37, changed to bech32 in Cosmos SDK 0.38 ([1])
+   * and changed back to type/value object in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly public_key: string | PubKey | null;
+  /**
+   * The account number assigned by the blockchain.
+   *
+   * This was string encoded in Cosmos SDK 0.37, changed to number in Cosmos SDK 0.38 ([1])
+   * and changed back to string in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly account_number: number | string;
+  /**
+   * The sequence number for replay protection.
+   *
+   * This was string encoded in Cosmos SDK 0.37, changed to number in Cosmos SDK 0.38 ([1])
+   * and changed back to string in Cosmos SDK 0.39 ([2]).
+   *
+   * [1]: https://github.com/cosmos/cosmos-sdk/pull/5280
+   * [2]: https://github.com/cosmos/cosmos-sdk/pull/6749
+   */
+  readonly sequence: number | string;
 }
 export interface AuthAccountsResponse {
   readonly height: string;
   readonly result: {
     readonly type: "cosmos-sdk/Account";
-    readonly value: CosmosSdkAccount;
+    readonly value: BaseAccount;
   };
 }
 export interface AuthExtension {
diff --git a/packages/sdk38/types/lcdapi/index.d.ts b/packages/sdk38/types/lcdapi/index.d.ts
index 6a06331d..07b83300 100644
--- a/packages/sdk38/types/lcdapi/index.d.ts
+++ b/packages/sdk38/types/lcdapi/index.d.ts
@@ -1,4 +1,4 @@
-export { AuthExtension, AuthAccountsResponse, setupAuthExtension } from "./auth";
+export { AuthExtension, AuthAccountsResponse, BaseAccount, setupAuthExtension } from "./auth";
 export { BankBalancesResponse, BankExtension, setupBankExtension } from "./bank";
 export {
   DistributionCommunityPoolResponse,
@@ -68,3 +68,4 @@ export {
   TxsResponse,
 } from "./base";
 export { LcdApiArray, LcdClient, normalizeLcdApiArray } from "./lcdclient";
+export { normalizePubkey, uint64ToNumber, uint64ToString } from "./utils";
diff --git a/packages/sdk38/types/lcdapi/utils.d.ts b/packages/sdk38/types/lcdapi/utils.d.ts
new file mode 100644
index 00000000..d3268564
--- /dev/null
+++ b/packages/sdk38/types/lcdapi/utils.d.ts
@@ -0,0 +1,22 @@
+import { PubKey } from "../types";
+/**
+ * Converts an integer expressed as number or string to a number.
+ * Throws if input is not a valid uint64 or if the value exceeds MAX_SAFE_INTEGER.
+ *
+ * This is needed for supporting Comsos SDK 0.37/0.38/0.39 with one client.
+ */
+export declare function uint64ToNumber(input: number | string): number;
+/**
+ * Converts an integer expressed as number or string to a string.
+ * Throws if input is not a valid uint64.
+ *
+ * This is needed for supporting Comsos SDK 0.37/0.38/0.39 with one client.
+ */
+export declare function uint64ToString(input: number | string): string;
+/**
+ * Normalizes a pubkey as in `BaseAccount.public_key` to allow supporting
+ * Comsos SDK 0.37–0.39.
+ *
+ * Returns null when unset.
+ */
+export declare function normalizePubkey(input: string | PubKey | null): PubKey | null;