diff --git a/.babelrc.js b/.babelrc.js
index 0368b0780..9d30fd373 100644
--- a/.babelrc.js
+++ b/.babelrc.js
@@ -16,14 +16,5 @@ module.exports = (api) => ({
     ],
     '@babel/preset-typescript',
   ],
-  plugins: [
-    '@babel/plugin-proposal-logical-assignment-operators',
-    api.env() === 'modules' && [
-      'transform-rename-import',
-      {
-        original: 'lodash',
-        replacement: 'lodash-es',
-      },
-    ],
-  ].filter(Boolean),
+  plugins: ['@babel/plugin-proposal-logical-assignment-operators'],
 });
diff --git a/package.json b/package.json
index f962f1eee..7bcbd8aad 100644
--- a/package.json
+++ b/package.json
@@ -73,6 +73,7 @@
     "@babel/core": "7.12.10",
     "@babel/plugin-proposal-logical-assignment-operators": "^7.12.1",
     "@babel/preset-typescript": "^7.12.7",
+    "@typescript-eslint/eslint-plugin": "^4.9.1",
     "@typescript-eslint/parser": "^4.9.1",
     "babel-core": "^7.0.0-bridge.0",
     "babel-eslint": "^10.1.0",
@@ -108,12 +109,9 @@
   },
   "dependencies": {
     "@babel/runtime": "^7.12.5",
-    "@types/lodash": "^4.14.165",
-    "@typescript-eslint/eslint-plugin": "^4.9.1",
-    "lodash": "^4.17.20",
-    "lodash-es": "^4.17.11",
     "nanoclone": "^0.2.1",
     "property-expr": "^2.0.4",
+    "tiny-case": "^1.0.1",
     "toposort": "^2.0.2"
   },
   "engines": {
diff --git a/rollup.config.js b/rollup.config.js
index a22b70e07..4ceda37e9 100644
--- a/rollup.config.js
+++ b/rollup.config.js
@@ -11,13 +11,7 @@ const base = {
       presets: [['jason', { modules: false, runtime: false }]],
     }),
   ],
-  external: [
-    'lodash/snakeCase',
-    'lodash/camelCase',
-    'toposort',
-    'fn-name',
-    'property-expr',
-  ],
+  external: ['toposort', 'fn-name', 'property-expr'],
 };
 
 module.exports = [
diff --git a/src/array.ts b/src/array.ts
index e9f7738b6..3d88cf753 100644
--- a/src/array.ts
+++ b/src/array.ts
@@ -9,7 +9,6 @@ import type {
   Callback,
   Message,
   Maybe,
-  Optionals,
 } from './types';
 import ValidationError from './ValidationError';
 import type Reference from './Reference';
@@ -21,7 +20,6 @@ import {
   SetFlag,
   Thunk,
   ToggleDefault,
-  TypeOf,
 } from './util/types';
 import BaseSchema, {
   AnySchema,
@@ -43,8 +41,8 @@ export function create<
 export default class ArraySchema<
   T extends AnySchema | Lazy<any, any>,
   C extends Config<any, any> = Config,
-  TIn extends Maybe<TypeOf<T>[]> = TypeOf<T>[] | undefined
-> extends BaseSchema<TIn, Asserts<T>[] | Optionals<TIn>, C> {
+  TIn extends Maybe<Asserts<T>[]> = Asserts<T>[] | undefined
+> extends BaseSchema<TIn, C> {
   innerType?: T;
 
   constructor(type?: T) {
@@ -288,8 +286,8 @@ create.prototype = ArraySchema.prototype;
 export default interface ArraySchema<
   T extends AnySchema | Lazy<any, any>,
   C extends Config<any, any> = Config,
-  TIn extends Maybe<TypeOf<T>[]> = TypeOf<T>[] | undefined
-> extends BaseSchema<TIn, Asserts<T>[] | Optionals<TIn>, C> {
+  TIn extends Maybe<Asserts<T>[]> = Asserts<T>[] | undefined
+> extends BaseSchema<TIn, C> {
   default<D extends Maybe<TIn>>(
     def: Thunk<D>,
   ): ArraySchema<T, ToggleDefault<C, D>, TIn>;
diff --git a/src/boolean.ts b/src/boolean.ts
index 99e0a4a34..6ea0036e6 100644
--- a/src/boolean.ts
+++ b/src/boolean.ts
@@ -22,7 +22,7 @@ export function create() {
 export default class BooleanSchema<
   TType extends Maybe<boolean> = boolean | undefined,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   constructor() {
     super({ type: 'boolean' });
 
@@ -73,7 +73,7 @@ create.prototype = BooleanSchema.prototype;
 export default interface BooleanSchema<
   TType extends Maybe<boolean>,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   default<D extends Maybe<TType>>(
     def: Thunk<D>,
   ): BooleanSchema<TType, ToggleDefault<TConfig, D>>;
diff --git a/src/date.ts b/src/date.ts
index a05ef64fa..e56bb8a7f 100644
--- a/src/date.ts
+++ b/src/date.ts
@@ -30,7 +30,7 @@ export function create() {
 export default class DateSchema<
   TType extends Maybe<Date> = Date | undefined,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   static INVALID_DATE = invalidDate;
 
   constructor() {
@@ -106,7 +106,7 @@ create.INVALID_DATE = invalidDate;
 export default interface DateSchema<
   TType extends Maybe<Date>,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   default<D extends Maybe<TType>>(
     def: Thunk<D>,
   ): DateSchema<TType, ToggleDefault<TConfig, D>>;
diff --git a/src/index.ts b/src/index.ts
index 4e43f6d7d..c1bd848c4 100644
--- a/src/index.ts
+++ b/src/index.ts
@@ -43,7 +43,7 @@ type ObjectSchemaOf<T extends AnyObject> = ObjectSchema<
       : T[k] extends AnyObject
       ? // we can't use  ObjectSchema<{ []: SchemaOf<T[k]> }> b/c TS produces a union of two schema
         ObjectSchemaOf<T[k]>
-      : BaseSchema<T[k], T[k], Config>;
+      : BaseSchema<T[k], Config>;
   }
 >;
 
@@ -51,7 +51,7 @@ type SchemaOf<T> = T extends Array<infer E>
   ? ArraySchema<SchemaOf<E>>
   : T extends AnyObject
   ? ObjectSchemaOf<T>
-  : BaseSchema<T, T, Config>;
+  : BaseSchema<T, Config>;
 
 export type AnyObjectSchema = ObjectSchema<any, any, any>;
 
diff --git a/src/mixed.ts b/src/mixed.ts
index 09fc4a469..1386de9cb 100644
--- a/src/mixed.ts
+++ b/src/mixed.ts
@@ -5,7 +5,7 @@ import BaseSchema from './schema';
 export declare class MixedSchema<
   TType = any,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   default<D extends Maybe<TType>>(
     def: Thunk<D>,
   ): MixedSchema<TType, ToggleDefault<TConfig, D>>;
@@ -14,7 +14,7 @@ export declare class MixedSchema<
     schema: MixedSchema<IT, IC>,
   ): MixedSchema<NonNullable<TType> | IT, TConfig & IC>;
   concat<IT, IC extends Config<any, any>>(
-    schema: BaseSchema<IT, any, IC>,
+    schema: BaseSchema<IT, IC>,
   ): MixedSchema<NonNullable<TType> | Optionals<IT>, TConfig & IC>;
   concat(schema: this): this;
 
diff --git a/src/number.ts b/src/number.ts
index bcfaecdf8..819871347 100644
--- a/src/number.ts
+++ b/src/number.ts
@@ -28,7 +28,7 @@ export function create() {
 export default class NumberSchema<
   TType extends Maybe<number> = number | undefined,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   constructor() {
     super({ type: 'number' });
 
@@ -151,7 +151,7 @@ create.prototype = NumberSchema.prototype;
 export default interface NumberSchema<
   TType extends Maybe<number> = number | undefined,
   TConfig extends Config<any, any> = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   strip(): NumberSchema<TType, SetFlag<TConfig, 's'>>;
 
   default<D extends Maybe<TType>>(
diff --git a/src/object.ts b/src/object.ts
index f1e31f99b..07a400355 100644
--- a/src/object.ts
+++ b/src/object.ts
@@ -1,5 +1,4 @@
-import snakeCase from 'lodash/snakeCase';
-import camelCase from 'lodash/camelCase';
+import { camelCase, snakeCase } from 'tiny-case';
 import { getter } from 'property-expr';
 
 import { object as locale } from './locale';
@@ -75,7 +74,7 @@ export type AssertsShape<S extends ObjectShape> = MakePartial<
   {
     [K in keyof S]: FieldType<S[K], '__outputType'>;
   }
->;
+> & { [k: string]: any };
 
 export type PartialSchema<S extends ObjectShape> = {
   [K in keyof S]: S[K] extends BaseSchema ? ReturnType<S[K]['optional']> : S[K];
@@ -106,8 +105,8 @@ const defaultSort = sortByKeyOrder([]);
 export default class ObjectSchema<
   TShape extends ObjectShape,
   TConfig extends Config<any, any> = Config<AnyObject, 'd'>,
-  TIn extends Maybe<TypeOfShape<TShape>> = TypeOfShape<TShape> | undefined
-> extends BaseSchema<TIn, AssertsShape<TShape> | Optionals<TIn>, TConfig> {
+  TIn extends Maybe<AssertsShape<TShape>> = AssertsShape<TShape> | undefined
+> extends BaseSchema<TIn, TConfig> {
   fields: TShape = Object.create(null);
 
   spec!: ObjectSchemaSpec;
@@ -316,7 +315,7 @@ export default class ObjectSchema<
     ? ObjectSchema<
         TShape & S,
         TConfig & C,
-        TypeOfShape<TShape & S> | Optionals<IType>
+        AssertsShape<TShape & S> | Optionals<IType>
       >
     : never;
   concat(schema: this): this;
@@ -363,7 +362,7 @@ export default class ObjectSchema<
   private setFields<S extends ObjectShape>(
     shape: S,
     excludedEdges?: readonly string[],
-  ): ObjectSchema<S, TConfig, TypeOfShape<S> | Optionals<TIn>> {
+  ): ObjectSchema<S, TConfig, AssertsShape<S> | Optionals<TIn>> {
     let next = this.clone() as any;
     next.fields = shape;
 
@@ -406,7 +405,7 @@ export default class ObjectSchema<
   deepPartial(): ObjectSchema<
     DeepPartialSchema<TShape>,
     TConfig,
-    Optionals<TIn> | undefined | TypeOfShape<DeepPartialSchema<TShape>>
+    Optionals<TIn> | undefined | AssertsShape<DeepPartialSchema<TShape>>
   > {
     const partial: any = {};
     for (const [key, schema] of Object.entries(this.fields)) {
@@ -533,8 +532,8 @@ create.prototype = ObjectSchema.prototype;
 export default interface ObjectSchema<
   TShape extends ObjectShape,
   TConfig extends Config<any, any> = Config<AnyObject, 'd'>,
-  TIn extends Maybe<TypeOfShape<TShape>> = TypeOfShape<TShape> | undefined
-> extends BaseSchema<TIn, AssertsShape<TShape> | Optionals<TIn>, TConfig> {
+  TIn extends Maybe<AssertsShape<TShape>> = AssertsShape<TShape> | undefined
+> extends BaseSchema<TIn, TConfig> {
   default<D extends Maybe<AnyObject>>(
     def: Thunk<D>,
   ): ObjectSchema<TShape, ToggleDefault<TConfig, D>, TIn>;
diff --git a/src/schema.ts b/src/schema.ts
index 1509e6268..14459eeda 100644
--- a/src/schema.ts
+++ b/src/schema.ts
@@ -32,7 +32,7 @@ import { Config, Defined, Flags, SetFlag, Thunk, _ } from './util/types';
 
 export { Config };
 
-export type ConfigOf<T> = T extends AnySchema<any, any, infer C> ? C : never;
+export type ConfigOf<T> = T extends AnySchema<any, infer C> ? C : never;
 
 export type ContextOf<T> = ConfigOf<T>['context'];
 
@@ -61,11 +61,10 @@ export type SchemaOptions<TDefault> = {
   spec?: SchemaSpec<TDefault>;
 };
 
-export type AnySchema<
-  TType = any,
-  TOut = any,
-  C extends Config = any
-> = BaseSchema<TType, TOut, C>;
+export type AnySchema<TType = any, C extends Config = any> = BaseSchema<
+  TType,
+  C
+>;
 
 export interface CastOptions<C = {}> {
   parent?: any;
@@ -122,15 +121,14 @@ export interface SchemaDescription {
 
 export default abstract class BaseSchema<
   TType = any,
-  TOut = TType,
   TConfig extends Config<any, any> = Config
 > {
   readonly type: string;
 
   readonly __type!: TType;
-  readonly __outputType!: ResolveFlags<TOut, TConfig['flags']>;
-  readonly __flags!: TConfig['flags'];
+  readonly __outputType!: ResolveFlags<TType, TConfig['flags']>;
 
+  readonly __flags!: TConfig['flags'];
   readonly __isYupSchema__!: boolean;
 
   readonly deps: readonly string[] = [];
@@ -803,7 +801,7 @@ export default abstract class BaseSchema<
     return next;
   }
 
-  strip(strip = true): BaseSchema<TType, TOut, SetFlag<TConfig, 's'>> {
+  strip(strip = true): BaseSchema<TType, SetFlag<TConfig, 's'>> {
     let next = this.clone();
     next.spec.strip = strip;
     return next as any;
@@ -837,9 +835,8 @@ export default abstract class BaseSchema<
 }
 
 export default interface BaseSchema<
-  TType = any,
   // eslint-disable-next-line @typescript-eslint/no-unused-vars
-  TOut = TType,
+  TType = any,
   TConfig extends Config<any, any> = Config
 > {
   validateAt(
diff --git a/src/string.ts b/src/string.ts
index d51824cd3..ea2eb29fb 100644
--- a/src/string.ts
+++ b/src/string.ts
@@ -44,7 +44,7 @@ export { create };
 export default class StringSchema<
   TType extends Maybe<string> = string | undefined,
   TConfig extends AnyConfig = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   constructor() {
     super({ type: 'string' });
 
@@ -219,7 +219,7 @@ create.prototype = StringSchema.prototype;
 export default interface StringSchema<
   TType extends Maybe<string> = string | undefined,
   TConfig extends AnyConfig = Config
-> extends BaseSchema<TType, TType, TConfig> {
+> extends BaseSchema<TType, TConfig> {
   default<D extends Maybe<TType>>(
     def: Thunk<D>,
   ): StringSchema<TType, ToggleDefault<TConfig, D>>;
diff --git a/yarn.lock b/yarn.lock
index 7eed2383b..d311a0aa3 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1878,11 +1878,6 @@
   resolved "https://registry.yarnpkg.com/@types/json5/-/json5-0.0.29.tgz#ee28707ae94e11d2b827bcbe5270bcea7f3e71ee"
   integrity sha1-7ihweulOEdK4J7y+UnC86n8+ce4=
 
-"@types/lodash@^4.14.165":
-  version "4.14.165"
-  resolved "https://registry.yarnpkg.com/@types/lodash/-/lodash-4.14.165.tgz#74d55d947452e2de0742bad65270433b63a8c30f"
-  integrity sha512-tjSSOTHhI5mCHTy/OOXYIhi2Wt1qcbHmuXD1Ha7q70CgI/I71afO4XtLb/cVexki1oVYchpul/TOuu3Arcdxrg==
-
 "@types/minimatch@*":
   version "3.0.3"
   resolved "https://registry.yarnpkg.com/@types/minimatch/-/minimatch-3.0.3.tgz#3dca0e3f33b200fc7d1139c0cd96c1268cadfd9d"
@@ -7571,11 +7566,6 @@ locate-path@^5.0.0:
   dependencies:
     p-locate "^4.1.0"
 
-lodash-es@^4.17.11:
-  version "4.17.15"
-  resolved "https://registry.yarnpkg.com/lodash-es/-/lodash-es-4.17.15.tgz#21bd96839354412f23d7a10340e5eac6ee455d78"
-  integrity sha512-rlrc3yU3+JNOpZ9zj5pQtxnx2THmvRykwL4Xlxoa8I9lHBlVbbyPhgyPMioxVZ4NqyxaVVtaJnzsyOidQIhyyQ==
-
 lodash._reinterpolate@~3.0.0:
   version "3.0.0"
   resolved "https://registry.yarnpkg.com/lodash._reinterpolate/-/lodash._reinterpolate-3.0.0.tgz#0ccf2d89166af03b3663c796538b75ac6e114d9d"
@@ -7609,7 +7599,7 @@ lodash.templatesettings@^4.0.0:
   dependencies:
     lodash._reinterpolate "~3.0.0"
 
-lodash@^4.17.11, lodash@^4.17.12, lodash@^4.17.14, lodash@^4.17.15, lodash@^4.17.19, lodash@^4.17.20, lodash@^4.17.4, lodash@^4.2.1:
+lodash@^4.17.11, lodash@^4.17.12, lodash@^4.17.14, lodash@^4.17.15, lodash@^4.17.19, lodash@^4.17.4, lodash@^4.2.1:
   version "4.17.20"
   resolved "https://registry.yarnpkg.com/lodash/-/lodash-4.17.20.tgz#b44a9b6297bcb698f1c51a3545a2b3b368d59c52"
   integrity sha512-PlhdFcillOINfeV7Ni6oF1TAEayyZBoZ8bcshTHqOYJYlrqzRK5hagpagky5o4HfCzzd1TRkXPMFq6cKk9rGmA==
@@ -10889,6 +10879,11 @@ timers-browserify@^2.0.4:
   dependencies:
     setimmediate "^1.0.4"
 
+tiny-case@^1.0.1:
+  version "1.0.1"
+  resolved "https://registry.yarnpkg.com/tiny-case/-/tiny-case-1.0.1.tgz#06b6257c0a35c72e455e23f55bab7abfc8049d8a"
+  integrity sha512-4d4i5qze9WwU+eVXygm+naw4Dx1GQGvISKyFAdIriw5P08+YASWCgi1+iRhC3H32vv20c7r2NP4g6lalG9Uspw==
+
 title-case@^2.1.0:
   version "2.1.1"
   resolved "https://registry.yarnpkg.com/title-case/-/title-case-2.1.1.tgz#3e127216da58d2bc5becf137ab91dae3a7cd8faa"