diff --git a/packages/cursorless-engine/src/processTargets/targets/PositionTarget.ts b/packages/cursorless-engine/src/processTargets/targets/PositionTarget.ts
index a0180b078e..c25e91be73 100644
--- a/packages/cursorless-engine/src/processTargets/targets/PositionTarget.ts
+++ b/packages/cursorless-engine/src/processTargets/targets/PositionTarget.ts
@@ -44,8 +44,15 @@ export default class PositionTarget extends BaseTarget {
     if (
       this.insertionDelimiter === "\n" &&
       this.position === "after" &&
-      this.thatTarget.contentRange.isSingleLine
+      this.state.thatTarget!.contentRange.isSingleLine
     ) {
+      // If the target that we're wrapping is not a single line, then we
+      // want to compute indentation based on the entire target.  Otherwise,
+      // we allow the editor to determine how to perform indentation.
+      // Note that we use `this.state.thatTarget` rather than `this.thatTarget`
+      // because we don't really want the transitive `thatTarget` behaviour, as
+      // it's not really the "that" target that we're after; it's the target that
+      // we're wrapping.  Should rework this stuff as part of #803.
       return "insertLineAfter";
     }
 
diff --git a/packages/cursorless-vscode-e2e/src/suite/fixtures/cursorless-snippets/elseBranch.cursorless-snippets b/packages/cursorless-vscode-e2e/src/suite/fixtures/cursorless-snippets/elseBranch.cursorless-snippets
new file mode 100644
index 0000000000..e5e0e3c56d
--- /dev/null
+++ b/packages/cursorless-vscode-e2e/src/suite/fixtures/cursorless-snippets/elseBranch.cursorless-snippets
@@ -0,0 +1,22 @@
+{
+  "elseStatement": {
+    "definitions": [
+      {
+        "scope": {
+          "langIds": [
+            "python"
+          ]
+        },
+        "body": [
+          "else:",
+          "\t$body"
+        ]
+      }
+    ],
+    "description": "Else branch",
+    "variables": {
+      "body": {}
+    },
+    "insertionScopeTypes": ["branch"]
+  }
+}
diff --git a/packages/cursorless-vscode-e2e/src/suite/fixtures/recorded/positions/snipElseAfterThis.yml b/packages/cursorless-vscode-e2e/src/suite/fixtures/recorded/positions/snipElseAfterThis.yml
new file mode 100644
index 0000000000..755a0a533e
--- /dev/null
+++ b/packages/cursorless-vscode-e2e/src/suite/fixtures/recorded/positions/snipElseAfterThis.yml
@@ -0,0 +1,31 @@
+languageId: python
+command:
+  version: 5
+  spokenForm: snip else after this
+  action:
+    name: insertSnippet
+    args:
+      - {type: named, name: elseStatement}
+  targets:
+    - type: primitive
+      mark: {type: cursor}
+      modifiers:
+        - {type: position, position: after}
+  usePrePhraseSnapshot: true
+initialState:
+  documentContents: |
+    if True:
+        aaa = "bbb"
+  selections:
+    - anchor: {line: 1, character: 7}
+      active: {line: 1, character: 7}
+  marks: {}
+finalState:
+  documentContents: |
+    if True:
+        aaa = "bbb"
+    else:
+        
+  selections:
+    - anchor: {line: 3, character: 4}
+      active: {line: 3, character: 4}