diff --git a/README.md b/README.md
index 06066b87..68084f1e 100644
--- a/README.md
+++ b/README.md
@@ -179,7 +179,7 @@ for sponsoring the project.
 - [`ap`: Combine the success values of multiple Futures using a function](#ap)
 - [`and`: Logical *and* for Futures](#and)
 - [`or`: Logical *or* for Futures](#or)
-- [`finally`: Run a Future after the previous settles](#finally)
+- [`assume`: Continue with another Future after the previous settles](#assume)
 - [`race`: Race two Futures against each other](#race)
 - [`both`: Await both success values from two Futures](#both)
 - [`parallel`: Await all success values from many Futures](#parallel)
@@ -1036,7 +1036,7 @@ Returns a new Future which either rejects with the first rejection reason, or
 resolves with the last resolution value once and if both Futures resolve. We
 can use it if we want a computation to run only after another has succeeded.
 
-See also [`or`](#or) and [`finally`](#finally).
+See also [`or`](#or) and [`assume`](#assume).
 
 ```js
 Future.after(300, null)
@@ -1072,7 +1072,7 @@ Returns a new Future which either resolves with the first resolution value, or
 rejects with the last rejection value once and if both Futures reject. We can
 use it if we want a computation to run only if another has failed.
 
-See also [`and`](#and) and [`finally`](#finally).
+See also [`and`](#and) and [`assume`](#assume).
 
 ```js
 Future.rejectAfter(300, new Error('Failed'))
@@ -1091,53 +1091,45 @@ any([Future.reject(1), Future.after(20, 2), Future.of(3)]).value(console.log);
 //> 2
 ```
 
-#### finally
+#### assume
 
-<details><summary><code>finally :: Future a c -> Future a b -> Future a b</code></summary>
+<details><summary><code>assume :: Future c d -> Future a b -> Future c d</code></summary>
 
 ```hs
-finally                  ::               Future a c -> Future a b -> Future a b
-lastly                   ::               Future a c -> Future a b -> Future a b
-Future.prototype.finally :: Future a b ~> Future a c               -> Future a b
-Future.prototype.lastly  :: Future a b ~> Future a c               -> Future a b
+assume                  ::               Future c d -> Future a b -> Future c d
+Future.prototype.assume :: Future a b ~> Future c d               -> Future c d
 ```
 
 </details>
 
-Run a second Future after the first settles (successfully or unsuccessfully).
-Rejects with the rejection reason from the first or second Future, or resolves
-with the resolution value from the first Future. We can use this when we want
-a computation to run after another settles, successfully or unsuccessfully.
-
-If you're looking to clean up resources after running a computation which
-acquires them, you should use [`hook`](#hook), which has many more fail-safes
-in place.
-
-This function has an alias `lastly`, for environments where `finally` is
-reserved.
+Run a second Future after the first settles (successfully or unsuccessfully),
+assuming its state.
 
 See also [`and`](#and) and [`or`](#or).
 
 ```js
 Future.of('Hello')
-.finally(Future.of('All done!').map(console.log))
+.assume(Future.of('World!'))
 .fork(console.error, console.log);
-//> "All done!"
-//> "Hello"
+//> "World!"
+
+Future.reject('Hello')
+.assume(Future.of('World!'))
+.fork(console.error, console.log);
+//> "World!"
 ```
 
-Note that the *first* Future is given as the *last* argument to `Future.finally()`:
+Note that the *first* Future is given as the *last* argument to `Future.assume()`:
 
 ```js
 var program = S.pipe([
   Future.of,
-  Future.finally(Future.of('All done!').map(console.log)),
+  Future.assume(Future.of('World!')),
   Future.fork(console.error, console.log)
 ]);
 
 program('Hello');
-//> "All done!"
-//> "Hello"
+//> "World!"
 ```
 
 ### Consuming Futures
diff --git a/index.d.ts b/index.d.ts
index ec050573..3f5c909c 100644
--- a/index.d.ts
+++ b/index.d.ts
@@ -87,8 +87,8 @@ declare module 'fluture' {
     /** Attempt to extract the resolution value. See https://github.com/fluture-js/Fluture#extractright */
     extractRight(): Array<R>
 
-    /** Set up a cleanup Future to run after this one is done. See https://github.com/fluture-js/Fluture#finally */
-    finally(cleanup: FutureInstance<L, any>): FutureInstance<L, R>
+    /** Continue with another Future after this one settles. See https://github.com/fluture-js/Fluture#assume */
+    assume<LB, RB>(other: FutureInstance<LB, RB>): FutureInstance<LB, RB>
 
     /** Fold both branches into the resolution branch. See https://github.com/fluture-js/Fluture#fold */
     fold<L, RB>(lmapper: (reason: L) => RB, rmapper: (value: R) => RB): FutureInstance<L, RB>
@@ -99,9 +99,6 @@ declare module 'fluture' {
     /** Fork with exception recovery. See https://github.com/fluture-js/Fluture#forkCatch */
     forkCatch(recover: RecoverFunction, reject: RejectFunction<L>, resolve: ResolveFunction<R>): Cancel
 
-    /** Set up a cleanup Future to run after this one is done. See https://github.com/fluture-js/Fluture#finally */
-    lastly(cleanup: FutureInstance<L, any>): FutureInstance<L, R>
-
     /** Map over the resolution value in this Future. See https://github.com/fluture-js/Fluture#map */
     map<RB>(mapper: (value: R) => RB): FutureInstance<L, RB>
 
@@ -254,9 +251,9 @@ declare module 'fluture' {
   /** Returns true for Futures that will certainly never settle. See https://github.com/fluture-js/Fluture#isnever */
   export function isNever(value: any): boolean
 
-  /** Set up a cleanup Future to run after the given action has settled. See https://github.com/fluture-js/Fluture#lastly */
-  export function lastly<L, R>(cleanup: FutureInstance<L, any>, action: FutureInstance<L, R>): FutureInstance<L, R>
-  export function lastly<L, R>(cleanup: FutureInstance<L, any>): (action: FutureInstance<L, R>) => FutureInstance<L, R>
+  /** Continue with another Future after the previous settles. See https://github.com/fluture-js/Fluture#assume */
+  export function assume<L, R>(other: FutureInstance<L, R>, source: FutureInstance<any, any>): FutureInstance<L, R>
+  export function assume<L, R>(other: FutureInstance<L, R>): (source: FutureInstance<any, any>) => FutureInstance<L, R>
 
   /** Map over the resolution value of the given Future. See https://github.com/fluture-js/Fluture#map */
   export function map<L, RA, RB>(mapper: (value: RA) => RB, source: FutureInstance<L, RA>): FutureInstance<L, RB>
diff --git a/src/dispatchers/assume.mjs b/src/dispatchers/assume.mjs
new file mode 100644
index 00000000..bc07d726
--- /dev/null
+++ b/src/dispatchers/assume.mjs
@@ -0,0 +1,14 @@
+import {isFuture} from '../future';
+import {partial1} from '../internal/utils';
+import {throwInvalidFuture} from '../internal/throw';
+
+function assume$right(right, left){
+  if(!isFuture(left)) throwInvalidFuture('Future.assume', 1, left);
+  return left.assume(right);
+}
+
+export function assume(right, left){
+  if(!isFuture(right)) throwInvalidFuture('Future.assume', 0, right);
+  if(arguments.length === 1) return partial1(assume$right, right);
+  return assume$right(right, left);
+}
diff --git a/src/dispatchers/index.mjs b/src/dispatchers/index.mjs
index fdee88e1..49f5604c 100644
--- a/src/dispatchers/index.mjs
+++ b/src/dispatchers/index.mjs
@@ -6,7 +6,7 @@ export {chain} from './chain';
 
 export {mapRej} from './map-rej';
 export {chainRej} from './chain-rej';
-export {lastly, lastly as finally} from './lastly';
+export {assume} from './assume';
 
 export {and} from './and';
 export {both} from './both';
diff --git a/src/dispatchers/lastly.mjs b/src/dispatchers/lastly.mjs
deleted file mode 100644
index 1dfe71fa..00000000
--- a/src/dispatchers/lastly.mjs
+++ /dev/null
@@ -1,14 +0,0 @@
-import {isFuture} from '../future';
-import {partial1} from '../internal/utils';
-import {throwInvalidFuture} from '../internal/throw';
-
-function lastly$right(right, left){
-  if(!isFuture(left)) throwInvalidFuture('Future.finally', 1, left);
-  return left.finally(right);
-}
-
-export function lastly(right, left){
-  if(!isFuture(right)) throwInvalidFuture('Future.finally', 0, right);
-  if(arguments.length === 1) return partial1(lastly$right, right);
-  return lastly$right(right, left);
-}
diff --git a/src/future.mjs b/src/future.mjs
index 77377ac1..7c1f0f11 100644
--- a/src/future.mjs
+++ b/src/future.mjs
@@ -616,16 +616,10 @@ defineBimapperAction('fold', {
   rejected: function FoldAction$rejected(x){ return mapWith(this.lmapper, resolve, x) }
 });
 
-var finallyAction = {
-  cancel: function FinallyAction$cancel(){ this.other._interpret(noop, noop, noop)() },
-  rejected: function FinallyAction$rejected(x){ return this.other._and(new Rejected(x)) },
-  resolved: function FinallyAction$resolved(x){
-    return this.other._map(function FoldAction$resolved$mapper(){ return x });
-  }
-};
-
-defineOtherAction('finally', finallyAction);
-defineOtherAction('lastly', finallyAction);
+defineOtherAction('assume', {
+  rejected: returnOther,
+  resolved: returnOther
+});
 
 defineOtherAction('and', {
   resolved: returnOther
diff --git a/test.js b/test.js
index f2e408a7..fd2a856c 100644
--- a/test.js
+++ b/test.js
@@ -21,7 +21,7 @@ import './test/5.chain.test.mjs';
 import './test/5.encase-n.test.mjs';
 import './test/5.encase-p.test.mjs';
 import './test/5.encase.test.mjs';
-import './test/5.finally.test.mjs';
+import './test/5.assume.test.mjs';
 import './test/5.fold.test.mjs';
 import './test/5.hook.test.mjs';
 import './test/5.map-rej.test.mjs';
diff --git a/test/2.transformation.test.mjs b/test/2.transformation.test.mjs
index 8d94525f..4e69c1dc 100644
--- a/test/2.transformation.test.mjs
+++ b/test/2.transformation.test.mjs
@@ -340,9 +340,9 @@ describe('Transformation', function (){
 
   });
 
-  describe('finally', function (){
+  describe('assume', function (){
 
-    var seq = dummy.finally(dummy);
+    var seq = dummy.assume(dummy);
 
     describe('#_interpret()', function (){
 
@@ -352,7 +352,7 @@ describe('Transformation', function (){
 
       it('runs the other if the left rejects', function (done){
         var other = Future(function (){done()});
-        var m = new Transformation(rejected, nil).finally(other);
+        var m = new Transformation(rejected, nil).assume(other);
         m._interpret(done, noop, noop);
       });
 
@@ -361,7 +361,7 @@ describe('Transformation', function (){
     describe('#toString()', function (){
 
       it('returns code to create the same data-structure', function (){
-        expect(seq.toString()).to.equal('Future.of("resolved").finally(Future.of("resolved"))');
+        expect(seq.toString()).to.equal('Future.of("resolved").assume(Future.of("resolved"))');
       });
 
     });
diff --git a/test/5.assume.test.mjs b/test/5.assume.test.mjs
new file mode 100644
index 00000000..f35f0a80
--- /dev/null
+++ b/test/5.assume.test.mjs
@@ -0,0 +1,109 @@
+import chai from 'chai';
+import {Future, assume, of, reject} from '../index.mjs';
+import * as U from './util';
+import * as F from './futures';
+import type from 'sanctuary-type-identifiers';
+
+var expect = chai.expect;
+
+var testInstance = function (assume){
+
+  it('is considered a member of fluture/Fluture', function (){
+    expect(type(assume(of(1), of(2)))).to.equal(Future['@@type']);
+  });
+
+  describe('#_interpret()', function (){
+
+    it('runs the second Future when the first resolves', function (done){
+      assume(of(1), of(null).map(done))._interpret(done, U.noop, U.noop);
+    });
+
+    it('runs the second Future when the first rejects', function (done){
+      assume(reject(1), of(null).map(done))._interpret(done, U.noop, U.noop);
+    });
+
+    it('always rejects with the rejection reason of the second', function (){
+      var actualResolved = assume(of(1), reject(2));
+      var actualRejected = assume(reject(1), reject(2));
+      return Promise.all([
+        U.assertRejected(actualResolved, 2),
+        U.assertRejected(actualRejected, 2)
+      ]);
+    });
+
+    it('always resolves with the resolution value of the second', function (){
+      var actualResolved = assume(of(1), of(2));
+      var actualRejected = assume(reject(1), of(2));
+      return Promise.all([
+        U.assertResolved(actualResolved, 2),
+        U.assertResolved(actualRejected, 2)
+      ]);
+    });
+
+    it('does nothing after being cancelled', function (done){
+      assume(F.resolvedSlow, F.resolved)._interpret(done, U.failRej, U.failRes)();
+      assume(F.resolved, F.resolvedSlow)._interpret(done, U.failRej, U.failRes)();
+      assume(F.rejectedSlow, F.rejected)._interpret(done, U.failRej, U.failRes)();
+      assume(F.rejected, F.rejectedSlow)._interpret(done, U.failRej, U.failRes)();
+      setTimeout(done, 25);
+    });
+
+  });
+
+};
+
+describe('assume()', function (){
+
+  it('is a curried binary function', function (){
+    expect(assume).to.be.a('function');
+    expect(assume.length).to.equal(2);
+    expect(assume(of(1))).to.be.a('function');
+  });
+
+  it('throws when not given a Future as first argument', function (){
+    var f = function (){ return assume(1) };
+    expect(f).to.throw(TypeError, /Future.*first/);
+  });
+
+  it('throws when not given a Future as second argument', function (){
+    var f = function (){ return assume(of(1), 1) };
+    expect(f).to.throw(TypeError, /Future.*second/);
+  });
+
+  testInstance(function (a, b){ return assume(b, a) });
+
+});
+
+describe('Future#assume()', function (){
+
+  it('throws when invoked out of context', function (){
+    var f = function (){ return of(1).assume.call(null, of(1)) };
+    expect(f).to.throw(TypeError, /Future/);
+  });
+
+  it('throws TypeError when not given a Future', function (){
+    var xs = [NaN, {}, [], 1, 'a', new Date, undefined, null, function (x){ return x }];
+    var fs = xs.map(function (x){ return function (){ return of(1).assume(x) } });
+    fs.forEach(function (f){ return expect(f).to.throw(TypeError, /Future/) });
+  });
+
+  testInstance(function (a, b){ return a.assume(b) });
+
+});
+
+describe('Future#assume()', function (){
+
+  it('throws when invoked out of context', function (){
+    var f = function (){ return of(1).assume.call(null, of(1)) };
+    expect(f).to.throw(TypeError, /Future/);
+  });
+
+  it('throws TypeError when not given a Future', function (){
+    var xs = [NaN, {}, [], 1, 'a', new Date, undefined, null, function (x){ return x }];
+    var fs = xs.map(function (x){ return function (){ return of(1).assume(x) } });
+    fs.forEach(function (f){ return expect(f).to.throw(TypeError, /Future/) });
+  });
+
+  testInstance(function (a, b){ return a.assume(b) });
+
+});
diff --git a/test/5.finally.test.mjs b/test/5.finally.test.mjs
deleted file mode 100644
index c4167d78..00000000
--- a/test/5.finally.test.mjs
+++ /dev/null
@@ -1,115 +0,0 @@
-import chai from 'chai';
-import {Future, lastly, of, reject} from '../index.mjs';
-import * as U from './util';
-import * as F from './futures';
-import type from 'sanctuary-type-identifiers';
-
-var expect = chai.expect;
-
-var testInstance = function (fin){
-
-  it('is considered a member of fluture/Fluture', function (){
-    expect(type(fin(of(1), of(2)))).to.equal(Future['@@type']);
-  });
-
-  describe('#_interpret()', function (){
-
-    it('runs the second Future when the first resolves', function (done){
-      fin(of(1), of(null).map(done))._interpret(done, U.noop, U.noop);
-    });
-
-    it('runs the second Future when the first rejects', function (done){
-      fin(reject(1), of(null).map(done))._interpret(done, U.noop, U.noop);
-    });
-
-    it('resolves with the resolution value of the first', function (){
-      var actual = fin(of(1), of(2));
-      return U.assertResolved(actual, 1);
-    });
-
-    it('rejects with the rejection reason of the first if the second resolves', function (){
-      var actual = fin(reject(1), of(2));
-      return U.assertRejected(actual, 1);
-    });
-
-    it('always rejects with the rejection reason of the second', function (){
-      var actualResolved = fin(of(1), reject(2));
-      var actualRejected = fin(reject(1), reject(2));
-      return Promise.all([
-        U.assertRejected(actualResolved, 2),
-        U.assertRejected(actualRejected, 2)
-      ]);
-    });
-
-    it('does nothing after being cancelled', function (done){
-      fin(F.resolvedSlow, F.resolved)._interpret(done, U.failRej, U.failRes)();
-      fin(F.resolved, F.resolvedSlow)._interpret(done, U.failRej, U.failRes)();
-      fin(F.rejectedSlow, F.rejected)._interpret(done, U.failRej, U.failRes)();
-      fin(F.rejected, F.rejectedSlow)._interpret(done, U.failRej, U.failRes)();
-      setTimeout(done, 25);
-    });
-
-    it('immediately runs and cancels the disposal Future when cancelled early', function (done){
-      var cancel = fin(F.resolvedSlow, Future(function (){ return function (){ return done() } }))._interpret(done, U.failRej, U.failRes);
-      setTimeout(cancel, 10);
-    });
-
-  });
-
-};
-
-describe('finally()', function (){
-
-  it('is a curried binary function', function (){
-    expect(lastly).to.be.a('function');
-    expect(lastly.length).to.equal(2);
-    expect(lastly(of(1))).to.be.a('function');
-  });
-
-  it('throws when not given a Future as first argument', function (){
-    var f = function (){ return lastly(1) };
-    expect(f).to.throw(TypeError, /Future.*first/);
-  });
-
-  it('throws when not given a Future as second argument', function (){
-    var f = function (){ return lastly(of(1), 1) };
-    expect(f).to.throw(TypeError, /Future.*second/);
-  });
-
-  testInstance(function (a, b){ return lastly(b, a) });
-
-});
-
-describe('Future#finally()', function (){
-
-  it('throws when invoked out of context', function (){
-    var f = function (){ return of(1).finally.call(null, of(1)) };
-    expect(f).to.throw(TypeError, /Future/);
-  });
-
-  it('throws TypeError when not given a Future', function (){
-    var xs = [NaN, {}, [], 1, 'a', new Date, undefined, null, function (x){ return x }];
-    var fs = xs.map(function (x){ return function (){ return of(1).finally(x) } });
-    fs.forEach(function (f){ return expect(f).to.throw(TypeError, /Future/) });
-  });
-
-  testInstance(function (a, b){ return a.finally(b) });
-
-});
-
-describe('Future#lastly()', function (){
-
-  it('throws when invoked out of context', function (){
-    var f = function (){ return of(1).lastly.call(null, of(1)) };
-    expect(f).to.throw(TypeError, /Future/);
-  });
-
-  it('throws TypeError when not given a Future', function (){
-    var xs = [NaN, {}, [], 1, 'a', new Date, undefined, null, function (x){ return x }];
-    var fs = xs.map(function (x){ return function (){ return of(1).lastly(x) } });
-    fs.forEach(function (f){ return expect(f).to.throw(TypeError, /Future/) });
-  });
-
-  testInstance(function (a, b){ return a.lastly(b) });
-
-});