diff --git a/src/components/views/dialogs/InviteDialog.tsx b/src/components/views/dialogs/InviteDialog.tsx
index 81a403bacf..c07cdf332b 100644
--- a/src/components/views/dialogs/InviteDialog.tsx
+++ b/src/components/views/dialogs/InviteDialog.tsx
@@ -6,9 +6,8 @@ SPDX-License-Identifier: AGPL-3.0-only OR GPL-3.0-only OR LicenseRef-Element-Com
 Please see LICENSE files in the repository root for full details.
 */
 
-import React, { type JSX, createRef, type ReactNode, type SyntheticEvent } from "react";
-import classNames from "classnames";
-import { RoomMember, type Room, MatrixError, EventType } from "matrix-js-sdk/src/matrix";
+import React, { createRef, type JSX, type ReactNode, type SyntheticEvent } from "react";
+import { EventType, MatrixError, type Room, RoomMember } from "matrix-js-sdk/src/matrix";
 import { KnownMembership } from "matrix-js-sdk/src/types";
 import { type MatrixCall } from "matrix-js-sdk/src/webrtc/call";
 import { logger } from "matrix-js-sdk/src/logger";
@@ -1260,30 +1259,89 @@ export default class InviteDialog extends React.PureComponent<Props, IInviteDial
         });
     }
 
-    public render(): React.ReactNode {
+    private hasSelection(): boolean {
+        return this.state.targets.length > 0 || (!!this.state.filterText && this.state.filterText.includes("@"));
+    }
+
+    /**
+     * Render the "suggestions" section, which shows a list of people you might want to invite, together with any
+     * errors from the previous iteration.
+     */
+    private renderSuggestions(): JSX.Element {
+        // If we're starting a DM, add a footer which showing our matrix.to link, for copying & pasting.
+        let footer;
+        if (this.props.kind === InviteKind.Dm) {
+            const link = makeUserPermalink(MatrixClientPeg.safeGet().getSafeUserId());
+            footer = (
+                <div className="mx_InviteDialog_footer">
+                    <h3>{_t("invite|send_link_prompt")}</h3>
+                    <CopyableText getTextToCopy={() => makeUserPermalink(MatrixClientPeg.safeGet().getSafeUserId())}>
+                        <a className="mx_InviteDialog_footer_link" href={link} onClick={this.onLinkClick}>
+                            {link}
+                        </a>
+                    </CopyableText>
+                </div>
+            );
+        }
+
+        let results: React.ReactNode | null = null;
+        let onlyOneThreepidNote: React.ReactNode | null = null;
+
+        if (!this.canInviteMore() || (this.hasFilterAtLeastOneEmail() && !this.canInviteThirdParty())) {
+            // We are in DM case here, because of the checks in canInviteMore() / canInviteThirdParty().
+            // Show a note saying "Invites by email can only be sent one at a time".
+            onlyOneThreepidNote = <div className="mx_InviteDialog_oneThreepid">{_t("invite|email_limit_one")}</div>;
+        } else {
+            let extraSection;
+            if (this.props.kind === InviteKind.Dm) {
+                // Some extra words saying "Some suggestions may be hidden for privacy"
+                extraSection = (
+                    <div className="mx_InviteDialog_section_hidden_suggestions_disclaimer">
+                        <span>{_t("invite|suggestions_disclaimer")}</span>
+                        <p>{_t("invite|suggestions_disclaimer_prompt")}</p>
+                    </div>
+                );
+            }
+
+            results = (
+                <div className="mx_InviteDialog_userSections">
+                    {this.renderSection("recents")}
+                    {this.renderSection("suggestions")}
+                    {extraSection}
+                </div>
+            );
+        }
+
+        return (
+            <React.Fragment>
+                {this.renderIdentityServerWarning()}
+                <div className="error">{this.state.errorText}</div>
+                {onlyOneThreepidNote}
+                {results}
+                {footer}
+            </React.Fragment>
+        );
+    }
+
+    /**
+     * Render content of the common "users" tab that is shown whether we have a regular invite dialog or a
+     * "CallTransfer" one.
+     */
+    private renderMainTab(): JSX.Element {
         let spinner: JSX.Element | undefined;
         if (this.state.busy) {
             spinner = <Spinner w={20} h={20} />;
         }
 
-        let title;
         let helpText;
         let buttonText;
         let goButtonFn: (() => Promise<void>) | null = null;
-        let consultConnectSection;
-        let extraSection;
-        let footer;
 
         const identityServersEnabled = SettingsStore.getValue(UIFeature.IdentityServer);
 
-        const hasSelection =
-            this.state.targets.length > 0 || (this.state.filterText && this.state.filterText.includes("@"));
-
         const cli = MatrixClientPeg.safeGet();
         const userId = cli.getUserId()!;
         if (this.props.kind === InviteKind.Dm) {
-            title = _t("space|add_existing_room_space|dm_heading");
-
             if (identityServersEnabled) {
                 helpText = _t(
                     "invite|start_conversation_name_email_mxid_prompt",
@@ -1316,34 +1374,10 @@ export default class InviteDialog extends React.PureComponent<Props, IInviteDial
 
             buttonText = _t("action|go");
             goButtonFn = this.checkProfileAndStartDm;
-            extraSection = (
-                <div className="mx_InviteDialog_section_hidden_suggestions_disclaimer">
-                    <span>{_t("invite|suggestions_disclaimer")}</span>
-                    <p>{_t("invite|suggestions_disclaimer_prompt")}</p>
-                </div>
-            );
-            const link = makeUserPermalink(MatrixClientPeg.safeGet().getSafeUserId());
-            footer = (
-                <div className="mx_InviteDialog_footer">
-                    <h3>{_t("invite|send_link_prompt")}</h3>
-                    <CopyableText getTextToCopy={() => makeUserPermalink(MatrixClientPeg.safeGet().getSafeUserId())}>
-                        <a className="mx_InviteDialog_footer_link" href={link} onClick={this.onLinkClick}>
-                            {link}
-                        </a>
-                    </CopyableText>
-                </div>
-            );
         } else if (this.props.kind === InviteKind.Invite) {
             const roomId = this.props.roomId;
             const room = MatrixClientPeg.get()?.getRoom(roomId);
             const isSpace = room?.isSpaceRoom();
-            title = isSpace
-                ? _t("invite|to_space", {
-                      spaceName: room?.name || _t("common|unnamed_space"),
-                  })
-                : _t("invite|to_room", {
-                      roomName: room?.name || _t("common|unnamed_room"),
-                  });
 
             let helpTextUntranslated;
             if (isSpace) {
@@ -1384,31 +1418,6 @@ export default class InviteDialog extends React.PureComponent<Props, IInviteDial
 
             buttonText = _t("action|invite");
             goButtonFn = this.inviteUsers;
-        } else if (this.props.kind === InviteKind.CallTransfer) {
-            title = _t("action|transfer");
-
-            consultConnectSection = (
-                <div className="mx_InviteDialog_transferConsultConnect">
-                    <label>
-                        <input type="checkbox" checked={this.state.consultFirst} onChange={this.onConsultFirstChange} />
-                        {_t("voip|transfer_consult_first_label")}
-                    </label>
-                    <AccessibleButton
-                        kind="secondary"
-                        onClick={this.onCancel}
-                        className="mx_InviteDialog_transferConsultConnect_pushRight"
-                    >
-                        {_t("action|cancel")}
-                    </AccessibleButton>
-                    <AccessibleButton
-                        kind="primary"
-                        onClick={this.transferCall}
-                        disabled={!hasSelection && this.state.dialPadValue === ""}
-                    >
-                        {_t("action|transfer")}
-                    </AccessibleButton>
-                </div>
-            );
         }
 
         const goButton =
@@ -1417,29 +1426,13 @@ export default class InviteDialog extends React.PureComponent<Props, IInviteDial
                     kind="primary"
                     onClick={goButtonFn}
                     className="mx_InviteDialog_goButton"
-                    disabled={this.state.busy || !hasSelection}
+                    disabled={this.state.busy || !this.hasSelection()}
                 >
                     {buttonText}
                 </AccessibleButton>
             );
 
-        let results: React.ReactNode | null = null;
-        let onlyOneThreepidNote: React.ReactNode | null = null;
-
-        if (!this.canInviteMore() || (this.hasFilterAtLeastOneEmail() && !this.canInviteThirdParty())) {
-            // We are in DM case here, because of the checks in canInviteMore() / canInviteThirdParty().
-            onlyOneThreepidNote = <div className="mx_InviteDialog_oneThreepid">{_t("invite|email_limit_one")}</div>;
-        } else {
-            results = (
-                <div className="mx_InviteDialog_userSections">
-                    {this.renderSection("recents")}
-                    {this.renderSection("suggestions")}
-                    {extraSection}
-                </div>
-            );
-        }
-
-        const usersSection = (
+        return (
             <React.Fragment>
                 <p className="mx_InviteDialog_helpText">{helpText}</p>
                 <div className="mx_InviteDialog_addressBar">
@@ -1449,102 +1442,155 @@ export default class InviteDialog extends React.PureComponent<Props, IInviteDial
                         {spinner}
                     </div>
                 </div>
-                {this.renderIdentityServerWarning()}
-                <div className="error">{this.state.errorText}</div>
-                {onlyOneThreepidNote}
-                {results}
-                {footer}
+                {this.renderSuggestions()}
             </React.Fragment>
         );
+    }
 
-        let dialogContent;
-        if (this.props.kind === InviteKind.CallTransfer) {
-            const tabs: NonEmptyArray<Tab<TabId>> = [
-                new Tab(
-                    TabId.UserDirectory,
-                    _td("invite|transfer_user_directory_tab"),
-                    "mx_InviteDialog_userDirectoryIcon",
-                    usersSection,
-                ),
-            ];
-
-            const backspaceButton = <DialPadBackspaceButton onBackspacePress={this.onDeletePress} />;
-
-            // Only show the backspace button if the field has content
-            let dialPadField;
-            if (this.state.dialPadValue.length !== 0) {
-                dialPadField = (
-                    <Field
-                        ref={this.numberEntryFieldRef}
-                        className="mx_InviteDialog_dialPadField"
-                        id="dialpad_number"
-                        value={this.state.dialPadValue}
-                        autoFocus={true}
-                        onChange={this.onDialChange}
-                        postfixComponent={backspaceButton}
-                    />
-                );
-            } else {
-                dialPadField = (
-                    <Field
-                        ref={this.numberEntryFieldRef}
-                        className="mx_InviteDialog_dialPadField"
-                        id="dialpad_number"
-                        value={this.state.dialPadValue}
-                        autoFocus={true}
-                        onChange={this.onDialChange}
-                    />
-                );
-            }
-
-            const dialPadSection = (
-                <div className="mx_InviteDialog_dialPad">
-                    <form onSubmit={this.onDialFormSubmit}>{dialPadField}</form>
-                    <Dialpad hasDial={false} onDigitPress={this.onDigitPress} onDeletePress={this.onDeletePress} />
-                </div>
-            );
-            tabs.push(
-                new Tab(
-                    TabId.DialPad,
-                    _td("invite|transfer_dial_pad_tab"),
-                    "mx_InviteDialog_dialPadIcon",
-                    dialPadSection,
-                ),
-            );
-            dialogContent = (
-                <React.Fragment>
-                    <TabbedView<TabId>
-                        tabs={tabs}
-                        activeTabId={this.state.currentTabId}
-                        tabLocation={TabLocation.TOP}
-                        onChange={this.onTabChange}
-                    />
-                    {consultConnectSection}
-                </React.Fragment>
-            );
-        } else {
-            dialogContent = (
-                <React.Fragment>
-                    {usersSection}
-                    {consultConnectSection}
-                </React.Fragment>
-            );
+    /**
+     * Render the complete dialog, given this is not a call transfer dialog.
+     *
+     * See also: {@link renderCallTransferDialog}.
+     */
+    private renderRegularDialog(): React.ReactNode {
+        let title;
+        if (this.props.kind === InviteKind.Dm) {
+            title = _t("space|add_existing_room_space|dm_heading");
+        } else if (this.props.kind === InviteKind.Invite) {
+            const roomId = this.props.roomId;
+            const room = MatrixClientPeg.get()?.getRoom(roomId);
+            const isSpace = room?.isSpaceRoom();
+            title = isSpace
+                ? _t("invite|to_space", {
+                      spaceName: room?.name || _t("common|unnamed_space"),
+                  })
+                : _t("invite|to_room", {
+                      roomName: room?.name || _t("common|unnamed_room"),
+                  });
         }
 
         return (
             <BaseDialog
-                className={classNames({
-                    mx_InviteDialog_transfer: this.props.kind === InviteKind.CallTransfer,
-                    mx_InviteDialog_other: this.props.kind !== InviteKind.CallTransfer,
-                    mx_InviteDialog_hasFooter: !!footer,
-                })}
+                className="mx_InviteDialog_other"
                 hasCancel={true}
                 onFinished={this.props.onFinished}
                 title={title}
                 screenName={this.screenName}
+            >
+                <div className="mx_InviteDialog_content">{this.renderMainTab()}</div>
+            </BaseDialog>
+        );
+    }
+
+    /**
+     * Render the complete call transfer dialog.
+     *
+     * See also: {@link renderRegularDialog}.
+     */
+    private renderCallTransferDialog(): React.ReactNode {
+        const usersSection = this.renderMainTab();
+
+        const tabs: NonEmptyArray<Tab<TabId>> = [
+            new Tab(
+                TabId.UserDirectory,
+                _td("invite|transfer_user_directory_tab"),
+                "mx_InviteDialog_userDirectoryIcon",
+                usersSection,
+            ),
+        ];
+
+        const backspaceButton = <DialPadBackspaceButton onBackspacePress={this.onDeletePress} />;
+
+        // Only show the backspace button if the field has content
+        let dialPadField;
+        if (this.state.dialPadValue.length !== 0) {
+            dialPadField = (
+                <Field
+                    ref={this.numberEntryFieldRef}
+                    className="mx_InviteDialog_dialPadField"
+                    id="dialpad_number"
+                    value={this.state.dialPadValue}
+                    autoFocus={true}
+                    onChange={this.onDialChange}
+                    postfixComponent={backspaceButton}
+                />
+            );
+        } else {
+            dialPadField = (
+                <Field
+                    ref={this.numberEntryFieldRef}
+                    className="mx_InviteDialog_dialPadField"
+                    id="dialpad_number"
+                    value={this.state.dialPadValue}
+                    autoFocus={true}
+                    onChange={this.onDialChange}
+                />
+            );
+        }
+
+        const dialPadSection = (
+            <div className="mx_InviteDialog_dialPad">
+                <form onSubmit={this.onDialFormSubmit}>{dialPadField}</form>
+                <Dialpad hasDial={false} onDigitPress={this.onDigitPress} onDeletePress={this.onDeletePress} />
+            </div>
+        );
+        tabs.push(
+            new Tab(TabId.DialPad, _td("invite|transfer_dial_pad_tab"), "mx_InviteDialog_dialPadIcon", dialPadSection),
+        );
+
+        const consultConnectSection = (
+            <div className="mx_InviteDialog_transferConsultConnect">
+                <label>
+                    <input type="checkbox" checked={this.state.consultFirst} onChange={this.onConsultFirstChange} />
+                    {_t("voip|transfer_consult_first_label")}
+                </label>
+                <AccessibleButton
+                    kind="secondary"
+                    onClick={this.onCancel}
+                    className="mx_InviteDialog_transferConsultConnect_pushRight"
+                >
+                    {_t("action|cancel")}
+                </AccessibleButton>
+                <AccessibleButton
+                    kind="primary"
+                    onClick={this.transferCall}
+                    disabled={!this.hasSelection() && this.state.dialPadValue === ""}
+                >
+                    {_t("action|transfer")}
+                </AccessibleButton>
+            </div>
+        );
+
+        const dialogContent = (
+            <React.Fragment>
+                <TabbedView<TabId>
+                    tabs={tabs}
+                    activeTabId={this.state.currentTabId}
+                    tabLocation={TabLocation.TOP}
+                    onChange={this.onTabChange}
+                />
+                {consultConnectSection}
+            </React.Fragment>
+        );
+
+        return (
+            <BaseDialog
+                className="mx_InviteDialog_transfer"
+                hasCancel={true}
+                onFinished={this.props.onFinished}
+                title={_t("action|transfer")}
+                screenName={this.screenName}
             >
                 <div className="mx_InviteDialog_content">{dialogContent}</div>
             </BaseDialog>
         );
     }
+
+    public render(): React.ReactNode {
+        if (this.props.kind === InviteKind.CallTransfer) {
+            return this.renderCallTransferDialog();
+        } else {
+            return this.renderRegularDialog();
+        }
+    }
 }