diff --git a/src/modules/menu/MenuModule.vue b/src/modules/menu/MenuModule.vue
index cd7728122..982ca3a7d 100644
--- a/src/modules/menu/MenuModule.vue
+++ b/src/modules/menu/MenuModule.vue
@@ -36,6 +36,8 @@ function toggleMenu() {
         <transition name="fade-in-out">
             <BlackBackdrop v-if="isPhoneMode && isMenuShown" @click="toggleMenu" />
         </transition>
+        <!-- NOTE: Below we need to use v-show and not v-if otherwise when the user toggle the full-screen while
+         editing a Report a problem window he will loose his content -->
         <HeaderWithSearch v-show="isHeaderShown" class="header" />
         <DebugToolbar v-if="hasDevSiteWarning" class="position-absolute end-0 debug-toolbar" />
         <div
diff --git a/src/modules/menu/components/header/HeaderWithSearch.vue b/src/modules/menu/components/header/HeaderWithSearch.vue
index 9d0f42758..d1fc41307 100644
--- a/src/modules/menu/components/header/HeaderWithSearch.vue
+++ b/src/modules/menu/components/header/HeaderWithSearch.vue
@@ -17,7 +17,7 @@
                 />
             </div>
             <div
-                class="search-bar-section d-flex-column flex-grow-1"
+                class="search-bar-section d-flex-column flex-grow-1 me-2"
                 :class="{ 'align-self-center': !hasDevSiteWarning }"
             >
                 <SearchBar />
diff --git a/src/modules/menu/components/search/SearchBar.vue b/src/modules/menu/components/search/SearchBar.vue
index a48923943..068dde846 100644
--- a/src/modules/menu/components/search/SearchBar.vue
+++ b/src/modules/menu/components/search/SearchBar.vue
@@ -3,11 +3,13 @@ import { computed, nextTick, onMounted, ref, watch } from 'vue'
 import { useStore } from 'vuex'
 
 import SearchResultList from '@/modules/menu/components/search/SearchResultList.vue'
+import log from '@/utils/logging'
 
 const dispatcher = { dispatcher: 'SearchBar' }
 
 const store = useStore()
 
+const isPristine = ref(true)
 const showResults = ref(false)
 const searchInput = ref(null)
 const searchValue = ref('')
@@ -20,8 +22,11 @@ const isPhoneMode = computed(() => store.getters.isPhoneMode)
 
 watch(hasResults, (newValue) => {
     // if an entry has been selected from the list, do not show the list again
-    // because the list has been hidden by onEntrySelected
-    if (!selectedEntry.value) {
+    // because the list has been hidden by onEntrySelected. Also if the search bar is pristine (not
+    // yet modified by the user) we don't want to show the result (e.g. at startup with a swisssearch
+    // query param)
+    if (!selectedEntry.value && !isPristine.value) {
+        log.debug(`Search has result changed to ${newValue}, change the show result to ${newValue}`)
         showResults.value = newValue
     }
 })
@@ -38,30 +43,28 @@ watch(searchQuery, (newQuery) => {
 
 onMounted(() => {
     searchValue.value = searchQuery.value
+    searchInput.value.focus()
 })
 
 let debounceSearch = null
 const updateSearchQuery = (event) => {
+    isPristine.value = false
     selectedEntry.value = null
     searchValue.value = event.target.value
 
+    if (hasResults.value) {
+        // we already have a result make sure to display it as soon as the user is typing
+        showResults.value = true
+    }
+
     clearTimeout(debounceSearch)
     debounceSearch = setTimeout(() => {
         store.dispatch('setSearchQuery', { query: event.target.value, ...dispatcher })
     }, 100)
 }
 
-const onSearchInputFocus = (event) => {
-    // When the focus event is due to a programatic focus event, the relatedTarget is not null
-    // and in this case we don't want to show the result. For example when selecting a result value
-    // we want to close the result and focus on the input, so that the user can directly change
-    // the search.
-    if (!event.relatedTarget && hasResults.value) {
-        showResults.value = true
-    }
-}
-
 const clearSearchQuery = () => {
+    hasResults.value = false
     showResults.value = false
     selectedEntry.value = null
     searchValue.value = ''
@@ -110,6 +113,16 @@ const toggleResults = () => {
         showResults.value = !showResults.value
     }
 }
+
+const onInputClicked = () => {
+    if (hasResults.value) {
+        if (isPhoneMode.value) {
+            showResults.value = !showResults.value
+        } else {
+            showResults.value = true
+        }
+    }
+}
 </script>
 
 <template>
@@ -137,12 +150,22 @@ const toggleResults = () => {
             :value="searchValue"
             data-cy="searchbar"
             tabindex="0"
+            @click="onInputClicked"
             @input="updateSearchQuery"
-            @focus="onSearchInputFocus"
             @keydown.down.prevent="goToFirstResult"
-            @keydown.esc.prevent="toggleResults"
+            @keydown.esc.prevent="clearSearchQuery"
             @keyup.enter.stop.prevent="goToFirstResult"
         />
+        <button
+            v-if="hasResults && !isPhoneMode"
+            class="btn btn-outline-group"
+            type="button"
+            tabindex="0"
+            data-cy="searchbar-toggle-result"
+            @click="toggleResults"
+        >
+            <FontAwesomeIcon :icon="showResults ? 'caret-up' : 'caret-down'" />
+        </button>
         <button
             v-show="searchValue"
             id="clearSearchButton"
diff --git a/src/modules/menu/components/search/SearchResultList.vue b/src/modules/menu/components/search/SearchResultList.vue
index 5a1f0870d..540eb76ed 100644
--- a/src/modules/menu/components/search/SearchResultList.vue
+++ b/src/modules/menu/components/search/SearchResultList.vue
@@ -135,11 +135,11 @@ defineExpose({ focusFirstEntry })
             class="shadow-lg search-results bg-light"
             :class="{
                 'border-top border-bottom': isPhoneMode,
-                'border rounded-bottom': !isPhoneMode,
+                'rounded-bottom': !isPhoneMode,
             }"
             data-cy="search-results"
         >
-            <div class="search-results-inner">
+            <div class="search-results-inner" :class="{ 'rounded-bottom': !isPhoneMode }">
                 <SearchResultCategory
                     v-for="(category, index) in categories"
                     v-show="category.results.length > 0"
@@ -165,7 +165,8 @@ defineExpose({ focusFirstEntry })
 
 .search-results-container {
     position: fixed;
-    z-index: $zindex-menu-header;
+    // here we need -1 in order to have the focus highlight of the search on top of the result
+    z-index: calc($zindex-menu-header - 1);
     top: $header-height;
     // 45vh (so that previews are visible), but on small screen min 20rem (ca. 3 lines per category)
     height: min(calc(100vh - $header-height), max(20rem, 45vh));
diff --git a/tests/cypress/tests-e2e/search/search-results.cy.js b/tests/cypress/tests-e2e/search/search-results.cy.js
index 69eee6aa2..17d9247b2 100644
--- a/tests/cypress/tests-e2e/search/search-results.cy.js
+++ b/tests/cypress/tests-e2e/search/search-results.cy.js
@@ -171,8 +171,11 @@ describe('Test the search bar result handling', () => {
             'Checking that it reads the swisssearch URL param at startup and launch a search with its content'
         )
         cy.reload()
+        cy.waitMapIsReady()
         cy.wait(['@search-locations', '@search-layers'])
         cy.readStoreValue('state.search.query').should('eq', 'test')
+        cy.get('@locationSearchResults').should('not.be.visible')
+        cy.get(searchbarSelector).click()
         cy.get('@locationSearchResults').should('be.visible')
 
         cy.log('Checking that it displays layer results with info-buttons')
@@ -211,11 +214,20 @@ describe('Test the search bar result handling', () => {
         cy.get(searchbarSelector).paste('test')
         cy.wait(`@search-locations`)
 
-        cy.log('Toggling the search result with ESC')
+        cy.log('Clearing the search result with ESC')
         cy.get(searchbarSelector).trigger('keydown', { key: 'Escape' })
         cy.get('[data-cy="search-results"]').should('not.be.visible')
-        cy.get(searchbarSelector).trigger('keydown', { key: 'Escape' })
+        cy.get(searchbarSelector).should('have.value', '')
+
+        cy.log('Toggling the search result with caret button')
+        cy.viewport(600, 600)
+        cy.get(searchbarSelector).paste('test')
+        cy.wait(`@search-locations`)
+        cy.get('[data-cy="searchbar-toggle-result"]').should('be.visible').click()
+        cy.get('[data-cy="search-results"]').should('not.be.visible')
+        cy.get('[data-cy="searchbar-toggle-result"]').should('be.visible').click()
         cy.get('[data-cy="search-results"]').should('be.visible')
+        cy.viewport('iphone-se2')
 
         cy.log('Navigating with arrow UP/DOWN')
         cy.get(searchbarSelector).trigger('keydown', { key: 'ArrowDown' })