diff --git a/lib/sourcemap.js b/lib/sourcemap.js
index 2feec45d..72c4709a 100644
--- a/lib/sourcemap.js
+++ b/lib/sourcemap.js
@@ -70,12 +70,27 @@ function SourceMap(options) {
     return {
         add: function(source, gen_line, gen_col, orig_line, orig_col, name) {
             var map = maps && maps[source];
+            var generatedPos = {
+                line: gen_line + options.dest_line_diff,
+                column: gen_col
+            };
             if (map) {
                 var info = map.originalPositionFor({
                     line: orig_line,
                     column: orig_col
                 });
-                if (info.source === null) return;
+                if (info.source === null) {
+                    if (generatedPos.column !== 0) {
+                        generator.
+                        generator.addMapping({
+                            generated: generatedPos,
+                            original: null,
+                            source: null,
+                            name: null
+                        });
+                    }
+                    return;
+                }
                 source = info.source;
                 orig_line = info.line;
                 orig_col = info.column;
@@ -84,10 +99,7 @@ function SourceMap(options) {
             generator.addMapping({
                 name: name,
                 source: source,
-                generated: {
-                    line: gen_line + options.dest_line_diff,
-                    column: gen_col
-                },
+                generated: generatedPos,
                 original: {
                     line: orig_line + options.orig_line_diff,
                     column: orig_col
diff --git a/test/input/pr-3040/expect.js b/test/input/pr-3040/expect.js
index b911f3f8..1b8674eb 100644
--- a/test/input/pr-3040/expect.js
+++ b/test/input/pr-3040/expect.js
@@ -1,2 +1,2 @@
 function _toConsumableArray(arr){if(Array.isArray(arr)){for(var i=0,arr2=Array(arr.length);i<arr.length;i++){arr2[i]=arr[i]}return arr2}else{return Array.from(arr)}}var _require=require("bar"),foo=_require.foo;var _require2=require("world"),hello=_require2.hello;foo.x.apply(foo,_toConsumableArray(foo.y(hello.z)));
-//# sourceMappingURL=data:application/json;charset=utf-8;base64,eyJ2ZXJzaW9uIjozLCJzb3VyY2VzIjpbImlucHV0Mi5qcyJdLCJuYW1lcyI6WyJyZXF1aXJlIiwiYXJyIl0sIm1hcHBpbmdzIjoiMEpBQWNBLEtBQVFDIiwic291cmNlc0NvbnRlbnQiOlsiY29uc3Qge2Zvb30gPSByZXF1aXJlKFwiYmFyXCIpO1xuY29uc3Qge2hlbGxvfSA9IHJlcXVpcmUoXCJ3b3JsZFwiKTtcblxuZm9vLngoLi4uZm9vLnkoaGVsbG8ueikpO1xuIl19
+//# sourceMappingURL=data:application/json;charset=utf-8;base64,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
diff --git a/test/input/pr-3040/input.js b/test/input/pr-3040/input.js
index 6515dcbd..39397953 100644
--- a/test/input/pr-3040/input.js
+++ b/test/input/pr-3040/input.js
@@ -8,4 +8,4 @@ var _require2 = require("world"),
 
 foo.x.apply(foo, _toConsumableArray(foo.y(hello.z)));
 
-//# sourceMappingURL=input.js.map
\ No newline at end of file
+//# sourceMappingURL=input.js.map
diff --git a/test/input/pr-3040/input.js.map b/test/input/pr-3040/input.js.map
index f0883e22..77ddeb28 100644
--- a/test/input/pr-3040/input.js.map
+++ b/test/input/pr-3040/input.js.map
@@ -1 +1 @@
-{"version":3,"sources":["input2.js"],"names":["require","foo","hello","x","apply","_toConsumableArray","y","z"],"mappings":"kLAAcA,QAAQ,OAAfC,aAAAA,kBACSD,QAAQ,SAAjBE,gBAAAA,MAEPD,IAAIE,EAAJC,MAAAH,IAAAI,mBAASJ,IAAIK,EAAEJ,MAAMK","sourcesContent":["const {foo} = require(\"bar\");\nconst {hello} = require(\"world\");\n\nfoo.x(...foo.y(hello.z));\n"]}
\ No newline at end of file
+{"version":3,"sources":["input2.js"],"names":[],"mappings":";;AAAA,IAAc;CAAP;;AACP,IAAgB;CAAT;;AAEP,iBAAM,mBAAG","sourcesContent":["const {foo} = require(\"bar\");\nconst {hello} = require(\"world\");\n\nfoo.x(...foo.y(hello.z));\n"]}
diff --git a/test/mocha/sourcemaps.js b/test/mocha/sourcemaps.js
index ccaa68e1..c2a5bd0a 100644
--- a/test/mocha/sourcemaps.js
+++ b/test/mocha/sourcemaps.js
@@ -1,6 +1,7 @@
 var assert = require("assert");
 var readFileSync = require("fs").readFileSync;
 var SourceMapConsumer = require("source-map").SourceMapConsumer;
+var SourceMapGenerator = require("source-map").SourceMapGenerator;
 var UglifyJS = require("../..");
 
 function read(path) {
@@ -284,5 +285,48 @@ describe("sourcemaps", function() {
                 assert.ok(pos.line <= 2, msg);
             });
         });
+
+        it("Should preserve unmapped segments in output source map", function() {
+            var generator = new SourceMapGenerator();
+
+            generator.addMapping({
+                source: "source.ts",
+                generated: {line: 1, column: 0},
+                original: {line: 1, column: 0},
+            });
+
+            generator.addMapping({
+                source: null,
+                original: null,
+                generated: {line: 1, column: 38}
+            });
+
+            generator.addMapping({
+                source: "source.ts",
+                generated: {line: 1, column: 51},
+                original: {line: 2, column: 0},
+            });
+
+            // Everything except the "say('hello');" part is mapped to "source.ts". The "say"
+            // function call is not mapped to any original source location. e.g. this can
+            // happen when a code transformer inserts generated code in between existing code.
+            var inputFile = "function say(msg) {console.log(msg)};say('hello');process.exit(1);";
+            var result = UglifyJS.minify(inputFile, {
+                sourceMap: {
+                    content: JSON.parse(generator.toString())
+                }
+            });
+
+            var transformedMap = new SourceMapConsumer(result.map);
+            var hasMappedSource = true;
+
+            for (let i = 0; i < result.code.length; i++) {
+                var info = transformedMap.originalPositionFor({line: 1, column: i});
+                hasMappedSource = hasMappedSource && !!info.source;
+            }
+
+            assert.equal(hasMappedSource, false, "Expected transformed source map to preserve the " +
+              "mapping without original source location");
+        });
     });
 });