diff --git a/test/assoc.test.ts b/test/assoc.test.ts
new file mode 100644
index 0000000..324b1cc
--- /dev/null
+++ b/test/assoc.test.ts
@@ -0,0 +1,147 @@
+import { expectType, expectError } from 'tsd';
+import { __, assoc } from '../es';
+
+type Obj = {
+  str: string;
+  num: number;
+};
+
+const obj: Obj = { str: 'foo', num: 1 };
+
+//
+// assoc(key)
+//
+
+// assoc(key)(__, obj)(val)
+expectType<Obj>(assoc('str')(__, obj)('bar'));
+// fails for wrong value type
+expectError(assoc('str')(__, obj)(2));
+// fails if key not unknown
+expectError(assoc('what')(__, obj)('bar'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('what')(__, {} as Record<string, number>)(2));
+
+// assoc(key)(val, obj)
+expectType<Obj>(assoc('str')('bar', obj));
+// fails for wrong value type
+expectError(assoc('str')(2, obj));
+// fails if key not unknown
+expectError(assoc('what')('bar', obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('what')(2, {} as Record<string, number>));
+
+// assoc(key)(val)(obj)
+expectType<Obj>(assoc('str')('bar')(obj));
+// fails for wrong value type
+expectError(assoc('str')(2)(obj));
+// fails if key not unknown
+expectError(assoc('what')('foo')(obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('what')(2)({} as Record<string, number>));
+
+
+//
+// assoc(__, val)
+//
+
+// assoc(__, val)(key)(obj)
+expectType<Obj>(assoc(__, 'bar')('str')(obj));
+// fails for wrong value type
+expectError(assoc(__, 2)('str')(obj));
+// fails if key not unknown
+expectError(assoc(__, 'bar')('what')(obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, 2)('what')({} as Record<string, number>));
+
+// assoc(__, val)(__, key)(obj)
+expectType<Obj>(assoc(__, 'bar')(__, obj)('str'));
+// fails for wrong value type
+expectError(assoc(__, 2)(__, obj)('str'));
+// fails if key not unknown
+expectError(assoc(__, 'bar')(__, obj)('what'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, 2)(__, {} as Record<string, number>)('str'));
+
+// assoc(__, val)(key, obj)
+expectType<Obj>(assoc(__, 'bar')('str', obj));
+// fails for wrong value type
+expectError(assoc(__, 2)('str', obj));
+// fails if key not unknown
+expectError(assoc(__, 'bar')('what', obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, 2)('str', {} as Record<string, number>));
+
+//
+// assoc(key, val)
+//
+
+// assoc(key, val)(obj)
+expectType<Obj>(assoc('str', 'bar')(obj));
+// fails for wrong value type
+expectError(assoc('str', 2)(obj));
+// fails if key not unknown
+expectError(assoc('what', 'bar')(obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('str', 2)({} as Record<string, number>));
+
+//
+// assoc__, __, obj)
+//
+
+// assoc(__, __, obj)(key)(val)
+expectType<Obj>(assoc(__, __, obj)('str')('bar'));
+// fails for wrong value type
+expectError(assoc(__, __, obj)('str')(2));
+// fails if key not unknown
+expectError(assoc(__, __, obj)('what')('bar'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, __, {} as Record<string, number>)('str')(2));
+
+// assoc(__, __, obj)(__, val)(key)
+expectType<Obj>(assoc(__, __, obj)(__, 'bar')('str'));
+// fails for wrong value type
+expectError(assoc(__, __, obj)(__, 2)('str'));
+// fails if key not unknown
+expectError(assoc(__, __, obj)(__, 'bar')('what'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, __, {} as Record<string, number>)(__, 2)('str'));
+
+// assoc(__, __, obj)(key, val)
+expectType<Obj>(assoc(__, __, obj)('str', 'bar'));
+// fails for wrong value type
+expectError(assoc(__, __, obj)('str', 2));
+// fails if key not unknown
+expectError(assoc(__, __, obj)('what', 'bar'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, __, {} as Record<string, number>)('str', 2));
+
+//
+// rest
+//
+
+// assoc(__, val, obj)(prop)
+expectType<Obj>(assoc(__,'bar', obj)('str'));
+// fails for wrong value type
+expectError(assoc(__, 2, obj)('str'));
+// fails if key not unknown
+expectError(assoc(__, 'bar', obj)('what'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc(__, 2, {} as Record<string, number>)('str'));
+
+// assoc(key, __, obj)(__, val)
+expectType<Obj>(assoc('str', __, obj)('bar'));
+// fails for wrong value type
+expectError(assoc('str', __, obj)(2));
+// fails if key not unknown
+expectError(assoc('what', __, obj)('bar'));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('str', __, {} as Record<string, number>)(2));
+
+// assoc(key, val, obj)
+expectType<Obj>(assoc('str', 'bar', obj));
+// fails for wrong value type
+expectError(assoc('str', 2, obj));
+// fails if key not unknown
+expectError(assoc('what', 'bar', obj));
+// Record<string, number> works as expected
+expectType<Record<string, number>>(assoc('str', 2, {} as Record<string, number>));
diff --git a/test/dissoc.test.ts b/test/dissoc.test.ts
new file mode 100644
index 0000000..639d1ed
--- /dev/null
+++ b/test/dissoc.test.ts
@@ -0,0 +1,65 @@
+import { expectType, expectError } from 'tsd';
+import { __, dissoc } from '../es';
+
+// `dissoc` does a `delete obj.key` under the hood, so the behavior for `dissoc` should make that
+type Obj = {
+  str: string;
+  num: number;
+  opt?: boolean;
+  orUndefined: boolean | undefined;
+  orNull: boolean | null;
+};
+
+const obj: Obj = { str: 'foo', num: 1, orUndefined: true, orNull: true };
+
+// must mark failed operations with ts-expect-error, otherwise `npm run test` fails
+// @ts-expect-error
+delete obj.str;
+// @ts-expect-error
+delete obj.num;
+delete obj.opt;
+delete obj.orUndefined;
+// @ts-expect-error
+delete obj.orNull;
+
+// only `opt` and `orUndefined` are allowed operations
+// `dissoc` should match that behavior
+
+expectError(dissoc('str', obj));
+expectError(dissoc('num', obj));
+expectType<Obj>(dissoc('opt', obj));
+expectType<Obj>(dissoc('orUndefined', obj));
+expectError(dissoc('orNull', obj));
+
+expectError(dissoc('str')(obj));
+expectError(dissoc('num')(obj));
+expectType<Obj>(dissoc('opt')(obj));
+expectType<Obj>(dissoc('orUndefined')(obj));
+expectError(dissoc('orNull')(obj));
+
+expectError(dissoc(__, obj)('str'));
+expectError(dissoc(__, obj)('num'));
+expectType<Obj>(dissoc(__, obj)('opt'));
+expectType<Obj>(dissoc(__, obj)('orUndefined'));
+expectError(dissoc(__, obj)('orNull'));
+
+// Record<string, number> is allowed
+const rec: Record<string, number> = { foo: 1, bar: 2 };
+
+// delete operation is ok for all keys
+delete rec.foo;
+delete rec.bar;
+delete rec.unknownKey;
+
+// and so are for `dissoc`
+dissoc('foo', rec);
+dissoc('bar', rec);
+dissoc('unknownKey', rec);
+
+dissoc('foo')(rec);
+dissoc('bar')(rec);
+dissoc('unknownKey')(rec);
+
+dissoc(__, rec)('foo');
+dissoc(__, rec)('bar');
+dissoc(__, rec)('unknownKey');
diff --git a/test/modify.test.ts b/test/modify.test.ts
new file mode 100644
index 0000000..dbf37d0
--- /dev/null
+++ b/test/modify.test.ts
@@ -0,0 +1,34 @@
+import { expectError, expectType } from 'tsd';
+
+import { modify, toUpper, add, identity, pipe, map } from '../es';
+
+type Obj = {
+  foo: string;
+  bar: number;
+};
+
+expectType<Obj>(modify('foo', toUpper, {} as Obj));
+expectType<Obj>(modify('bar', add(1), {} as Obj));
+expectType<Obj>(modify('foo', toUpper)({} as Obj));
+expectType<Obj>(modify('bar', add(1))({} as Obj));
+expectType<Obj>(modify('foo')(toUpper)({} as Obj));
+expectType<Obj>(modify('bar')(add(1))({} as Obj));
+expectType<Obj>(modify('foo')(toUpper, {} as Obj));
+expectType<Obj>(modify('bar')(add(1), {} as Obj));
+
+// fails when function has wrong argument type
+expectError(modify('foo', add(1), {} as Obj));
+expectError(modify('bar', toUpper, {} as Obj));
+
+// fails when key does not exist on Obj
+expectError(modify('unknownKey', toUpper, {} as Obj));
+
+// works with generic fn
+expectType<Obj>(modify('foo', identity, {} as Obj));
+
+// pipe and map sanity checks
+const f = pipe(
+  map<Obj, Obj>(modify('foo', toUpper))
+);
+
+expectType<Obj[]>(f([] as Obj[]));
diff --git a/types/assoc.d.ts b/types/assoc.d.ts
index 1814c87..853f670 100644
--- a/types/assoc.d.ts
+++ b/types/assoc.d.ts
@@ -1,73 +1,49 @@
 import { Placeholder } from './util/tools';
 
-// assoc(__, val, obj)(prop), this tests if prop is keyof obj and if val is typeof obj[prop] for best return type
-export function assoc<T, U>(__: Placeholder, val: T, obj: U): <K extends string>(prop: K) => K extends keyof U ? T extends U[K] ? U : Record<K, T> & Omit<U, K> : U & Record<K, T>;
-// assoc(prop, __, obj)(val), when K is keyof obj, tests if val is typeof obj[prop] for best return type
-export function assoc<U, K extends keyof U>(prop: K, __: Placeholder, obj: U): <T>(val: T) => T extends U[K] ? U : Record<K, T> & Omit<U, K>;
-// assoc(prop, __, obj)(val), when prop is not keyof obj
-export function assoc<U, K extends string>(prop: K, __: Placeholder, obj: U): <T>(val: T) => U & Record<K, T>;
-// assoc(prop, val, obj) when prop is keyof obj and val is same type
-export function assoc<K extends keyof U, U>(prop: K, val: U[K], obj: U): U;
-// assoc(prop, val, obj) when prop is keyof obj  and val is not same type
-export function assoc<T, K extends keyof U, U>(prop: K, val: T, obj: U): Record<K, T> & Omit<U, K>;
-// assoc(prop, val, obj) when prop is not keyof obj
-export function assoc<T, U, K extends string>(prop: K, val: T, obj: U): U & Record<K, T>;
+// assoc(prop)
+export function assoc<K extends PropertyKey>(prop: K): {
+  // assoc(prop)(val)(obj)
+  <T>(val: T): <U extends Record<K, T>>(obj: U) => U;
+
+  // assoc(prop)(__, obj)(val)
+  <U extends Record<K, any>>(__: Placeholder, obj: U): <T extends U[K]>(val: T) => U;
+
+  // assoc(prop)(val, obj) when obj has key prop, tests if val is typeof obj[prop] for best return type
+  <U extends Record<K, T>, T>(val: T, obj: U): U;
+};
 
 // assoc(__, val)
 export function assoc<T>(__: Placeholder, val: T) : {
-  // assoc(__, val)(__, obj)
-  <U>(__2: Placeholder, obj: U): {
-    // assoc(__, val)(__, obj)(prop), prop is keyof obj, tests if val is typeof obj[prop] for best return type
-    <K extends keyof U>(prop: K): U[K] extends T ? U : Record<K, T> & Omit<U, K>;
-    // assoc(__, val)(__, obj)(prop), prop is not keyof obj
-    <K extends string>(prop: K): U & Record<K, T>;
-  };
-  // assoc(__, val)(prop, obj), when obj has key prop, tests if val is typeof obj[prop] for best return type
-  <K extends keyof U, U>(prop: K, obj: U): U[K] extends T ? U : Record<K, T> & Omit<U, K>;
-  // assoc(__, val)(prop, obj), when obj does not have key prop
-  <K extends string, U>(prop: K, obj: U): U & Record<K, T>;
+  // assoc(__, val)(prop)(obj)
+  <K extends PropertyKey>(prop: K extends Placeholder ? never : K): <U extends Record<K, T>>(obj: U) => U;
 
-  // assoc(__, val)(prop)
-  <K extends string>(prop: K): {
-    // assoc(__, val)(prop)(obj) when obj has key prop, tests if val is typeof obj[prop] for best return type
-    <U extends Record<K, any>>(obj: U): U[K] extends T ? U : Record<K, T> & Omit<U, K>;
-    // assoc(__, val)(prop)(obj) when obj does not have key prop
-    <U>(obj: U): U & Record<K, T>;
-  }
-};
+  // assoc(__, val)(__, obj)(prop)
+  <U>(__2: Placeholder, obj: U): <K extends keyof U>(prop: T extends U[K] ? K : never) => U;
 
-// assoc(prop, val)
-export function assoc<T, K extends string>(prop: K, val: T) : {
-  // assoc(prop, val)(obj), when obj has key prop, tests if val is typeof obj[prop] for best return type
-  <U extends Record<K, any>>(obj: U): U[K] extends T ? U : Record<K, T> & Omit<U, K>;
-  // assoc(prop, val)(obj), when obj does not have key prop
-  <U>(obj: U): U & Record<K, T>;
+  // assoc(__, val)(prop, obj)
+  <U extends Record<K, T>, K extends keyof U>(prop: K, obj: U): U;
 };
 
-// assoc(prop)
-export function assoc<K extends string>(prop: K): {
-  // assoc(prop)(__, obj) when prop is keyof obj
-  <U extends Record<K, any>>(__: Placeholder, obj: U): {
-    // assoc(prop)(__, obj)(val) if val is typeof obj[prop]
-    <T extends U[K]>(val: T): U;
-    // assoc(prop)(__, obj)(val) if val is not typeof obj[prop]
-    <T>(val: T): Record<K, T> & Omit<U, K>;
-  }
-  // assoc(prop)(__, obj) when prop is not keyof obj
-  <U>(__: Placeholder, obj: U): <T>(val: T) => U & Record<K, T>;
+// assoc(prop, val)(obj)
+export function assoc<K extends PropertyKey, T>(prop: K extends Placeholder ? never : K, val: T): <U extends Record<K, T>>(obj: U) => U;
 
-  // assoc(prop)(val, obj) when obj has key prop, tests if val is typeof obj[prop] for best return type
-  <T, U extends Record<K, any>>(val: T, obj: U): U[K] extends T ? U : Record<K, T> & Omit<U, K>;
-  // assoc(prop)(val, obj) when obj does not have a key prop
-  <T, U>(val: T, obj: U): U & Record<K, T>;
+// assoc (__, __, obj)
+export function assoc<U>(__: Placeholder, __2: Placeholder, obj: U): {
+  // assoc(__, __, obj)(prop)(val)
+  <K extends keyof U>(prop: K extends Placeholder ? never : K): <T extends U[K]>(val: T) => U;
+
+  // assoc(__, __, obj)(__, val)(prop)
+  <T>(__: Placeholder, val: T): <K extends keyof U>(prop: T extends U[K] ? K : never) => U;
 
-  // assoc(prop)(val)
-  <T>(val: T): {
-    // assoc(prop)(val)(obj) when obj has key prop and val is typeof obj[prop]
-    <U extends Record<K, T>>(obj: U): U;
-    // assoc(prop)(val)(obj) when obj has key prop and val is not typeof obj[prop]
-    <U extends Record<K, any>>(obj: U): Record<K, T> & Omit<U, K>;
-    // assoc(prop)(val)(obj) when obj does not have key prop
-    <U>(obj: U): U & Record<K, T>;
-  }
+  // assoc(__, __, obj)(prop, val)
+  <K extends keyof U, T extends U[K]>(prop: K, val: T): U;
 };
+
+// assoc(__, val, obj)(prop)
+export function assoc<U, T extends U[keyof U]>(__: Placeholder, val: T, obj: U): <K extends keyof U>(prop: T extends U[K] ? K : never) => U;
+
+// assoc(prop, __, obj)(val)
+export function assoc<U, K extends keyof U>(prop: K, __: Placeholder, obj: U): <T extends U[K]>(val: T) => U;
+
+// assoc(prop, val, obj)
+export function assoc<U, K extends keyof U, T extends U[K]>(prop: K, val: T, obj: U): U;
diff --git a/types/dissoc.d.ts b/types/dissoc.d.ts
index 08533a4..3d1d680 100644
--- a/types/dissoc.d.ts
+++ b/types/dissoc.d.ts
@@ -1,2 +1,6 @@
-export function dissoc<K extends string | number>(prop: K): <T extends object>(obj: T) => Omit<T, K>;
-export function dissoc<T extends object, K extends keyof T>(prop: K, obj: T): Omit<T, K>;
+import { Placeholder } from './util/tools';
+
+// `string extends keyof U` is true only for `Record<string, T>`, where the keys are not known, something that still needs to be supported
+export function dissoc<K extends PropertyKey>(prop: K extends Placeholder ? never : K): <U extends { [P in K]?: any}>(obj: string extends keyof U ? U : undefined extends U[K] ? U : never) => U;
+export function dissoc<U>(__: Placeholder, obj: U): <K extends keyof U>(prop: string extends keyof U ? K : undefined extends U[K] ? K : never) => U;
+export function dissoc<U, K extends keyof U>(prop: string extends keyof U ? K : undefined extends U[K] ? K : never, obj: U): U;
diff --git a/types/modify.d.ts b/types/modify.d.ts
index fe9a229..28c0737 100644
--- a/types/modify.d.ts
+++ b/types/modify.d.ts
@@ -1,10 +1,13 @@
-export function modify<K extends string, A, P>(
-  prop: K,
-  fn: (a: A) => P,
-): <T extends Record<K, A>>(target: T) => Omit<T, K> & Record<K, P>;
+// modify(prop)
+export function modify<K extends PropertyKey>(prop: K): {
+  // modify(prop)(fn)(obj)
+  <T>(fn: (value: T) => T): <U extends Record<K, T>>(object: U) => U;
+  // modify(prop)(fn), obj)
+  <T, U extends Record<K, T>>(fn: (value: T) => T, object: U): U;
+};
 
-export function modify<T extends object, K extends keyof T, P>(
-  prop: K,
-  fn: (a: T[K]) => P,
-  obj: T,
-): Omit<T, K> & Record<K, P>;
+// modify(prop, fn)(obj)
+export function modify<K extends PropertyKey, T>(prop: K, fn: (value: T) => T): <U extends Record<K, T>>(object: U) => U;
+
+// modify(prop, fn, obj)
+export function modify<U, K extends keyof U>(prop: K, fn: (value: U[K]) => U[K], object: U): U;
diff --git a/types/util/tools.d.ts b/types/util/tools.d.ts
index c80c6d2..9d70ad3 100644
--- a/types/util/tools.d.ts
+++ b/types/util/tools.d.ts
@@ -501,6 +501,11 @@ export type WidenLiterals<T> =
         ? number
         : T;
 
+/**
+ * Alias for the common result type for the `assoc` function
+ */
+export type AssocResults<K extends PropertyKey, T, U> = U extends Record<K, any> ? T extends U[K] ? U : Omit<U, K> & Record<K, T> : Omit<U, K> & Record<K, T>;
+
 /**
  * Extract the types from an array
  * Works with Tuples, eg `ElementOf<typeof ['p1', 'p2']>` => `'p1' | 'p2'`