diff --git a/agent/BACKLOG.md b/agent/BACKLOG.md
index bdc5e1e..23b2e0f 100644
--- a/agent/BACKLOG.md
+++ b/agent/BACKLOG.md
@@ -26,23 +26,6 @@ next, in what order*.
 
 ## NEXT
 
-### 31. rofi search broken under rofi 2.0.0 `[bug]`
-(Raised by Bernardo, 2026-07-07.) Typing a lowercase query fails to
-match (`steam` doesn't select **Steam**) and Enter launches the first
-entry instead (ghostty) — i.e. matching behaves case-sensitively and the
-selection never moves off row 0. **Not a missing config key:** the
-generated config already sets `case-sensitive = false`, `matching =
-"fuzzy"`, `sort = true`, `sorting-method = "fzf"`, and `rofi -dump-config`
-shows rofi 2.0.0 honours them (they're its new defaults). The lock bump
-`8fded63` pulled **rofi 2.0.0** (a major version) — this is a 2.0
-behaviour change. Needs interactive repro on a session (can't be
-eyeballed headlessly). Candidate levers to A/B live: `matching`
-(normal/prefix vs fuzzy), `-i`/`case-smart`/`normalize-match` (new 2.0
-knobs), `sort`/`sorting-method`, and the per-modi `sorting-method:"name"`
-default 2.0 shows for drun. Fix once, then bake into
-`programs.rofi.extraConfig`. Covers Bernardo's item 1 (case-insensitive
-search).
-
 ### 32. SUPER+? cheatsheet bind still not opening `[bug]`
 (Raised by Bernardo, 2026-07-07 — item 2.) Item 26's fix (SHIFT in the
 bind modmask so the shifted `question` keysym fires) shipped, but SUPER+?
@@ -50,11 +33,6 @@ still doesn't open the keybindings cheatsheet. Re-diagnose: confirm the
 Hyprland bind's modmask/keysym against the *actual* layout, whether rofi
 2.0.0 changed anything, and that the cheatsheet path still resolves.
 
-### 39. Icons in the power-profile rofi menu
-(Raised by Bernardo, 2026-07-07 — item 9.) The power-profile picker
-(rofi.nix `power-profile`) lists profiles as bare text; add per-profile
-icons (performance/balanced/power-saver) like the other System rows.
-Small.
 
 ### 36. Battery / power quick menu
 (Raised by Bernardo, 2026-07-07 — items "battery toggle in a rofi
diff --git a/agent/HARDWARE-QUEUE.md b/agent/HARDWARE-QUEUE.md
index 1c26c54..6e0bc61 100644
--- a/agent/HARDWARE-QUEUE.md
+++ b/agent/HARDWARE-QUEUE.md
@@ -236,6 +236,13 @@ QA machine), the **T14s** (webcam case).
       unchanged (the bar still reserves its space). Accepted trade-off
       of `layer: bottom`: a floating window dragged over the top strip
       can now overlap the bar — confirm that's the only regression.
+- [ ] **rofi menu polish** (iteration #58, item 39 + #56/#57 34/40) —
+      after `home-update`: (a) menu › System › Power profile shows a
+      colored icon per profile (performance/balanced/power-saver), not
+      just text — icons *render* (not blank); (b) every submenu's ↩ Back
+      shows a single arrow, no double; (c) on this single-monitor box,
+      System › Display → pick a resolution → Back returns to System
+      (not back into the same resolution list).
 
 ## AMD dev box only
 - [ ] **AMD runtime bits** — VA-API (`vainfo` → radeonsi), amd-pstate EPP
diff --git a/agent/JOURNAL.md b/agent/JOURNAL.md
index 8647565..5b71ac9 100644
--- a/agent/JOURNAL.md
+++ b/agent/JOURNAL.md
@@ -17,6 +17,25 @@ Template:
 
 ---
 
+## 2026-07-07 — rofi search mis-ranks + power-profile icons (iteration #58, items 31 & 39)
+- **#31 (rofi search broken):** Bernardo ran the live A/B — `-sorting-method
+  normal` and `-matching normal` both fixed "steam"→Steam; `-no-sort` did
+  not. So the culprit is rofi 2.0.0's **fzf sorter** paired with fuzzy
+  matching (it ranked ghostty above Steam), not case-sensitivity. Fix:
+  `programs.rofi.extraConfig.sorting-method` `"fzf"` → `"normal"`, keeping
+  `matching="fuzzy"` (forgiveness) + `case-sensitive=false`. Also closes
+  Bernardo's batch item 1 (case-insensitive — already false, now ranks
+  right too).
+- **#39 (power-profile icons):** the picker listed profiles as bare text.
+  Now emits `row "$p" battery-profile-<p>` using Papirus' **colored**
+  `battery-profile-{performance,balanced,powersave}` family (the
+  `-symbolic` variants are #444 grey → invisible on dark themes; verified
+  the colored ones carry real fills). Returned row text stays the bare
+  profile name, so `powerprofilesctl set` is unaffected; added `-show-icons`.
+- **Verified:** V0 `nix flake check --no-build` green for both. #31's fix
+  is the exact lever Bernardo confirmed live. #39's icon *rendering* is a
+  V3 visual check (Papirus lookup can't be eyeballed headlessly) — queued.
+
 ## 2026-07-07 — Display menu "Back" doesn't return (iteration #57, item 40)
 - **Task:** BACKLOG item 40 — in System › Display the Back row didn't
   return on a single-monitor machine.
diff --git a/modules/home/rofi.nix b/modules/home/rofi.nix
index 3e9e572..152290e 100644
--- a/modules/home/rofi.nix
+++ b/modules/home/rofi.nix
@@ -227,8 +227,22 @@ let
           exit 0
         fi
         cur=$(powerprofilesctl get 2>/dev/null)
-        choice=$( { powerprofilesctl list 2>/dev/null | sed -nE 's/^[* ] ([a-z-]+):$/\1/p'; printf '%s\n' "$BACK"; } \
-          | rofi -dmenu -p "profile (now: $cur)") || exit 0
+        # Each profile gets its themed icon from Papirus' colored
+        # battery-profile-* family (the -symbolic variants are #444 grey and
+        # vanish on dark themes). The selected row's returned text is still
+        # the bare profile name, so `powerprofilesctl set` is unaffected.
+        choice=$( {
+          powerprofilesctl list 2>/dev/null | sed -nE 's/^[* ] ([a-z-]+):$/\1/p' \
+            | while IFS= read -r p; do
+                case "$p" in
+                  performance) row "$p" battery-profile-performance ;;
+                  balanced)    row "$p" battery-profile-balanced ;;
+                  power-saver) row "$p" battery-profile-powersave ;;
+                  *)           row "$p" preferences-system-power ;;
+                esac
+              done
+          back
+        } | rofi -dmenu -show-icons -p "profile (now: $cur)") || exit 0
         [ "$choice" = "$BACK" ] && exec "$0" system
         [ -n "$choice" ] && powerprofilesctl set "$choice" ;;
 
@@ -899,13 +913,20 @@ in
         # while the app launcher still fills + scrolls past `lines`.
         fixed-num-lines = false;
         # Search: case-insensitive fuzzy across every menu + the launcher, so
-        # "system" finds "System" and "fzr" finds "Firefox". fzf sorting ranks
-        # the closest match to the top (the per-keystroke modules — calc/emoji
-        # — opt out per-invocation with -no-sort).
+        # "system" finds "System" and "fzr" finds "Firefox". `normal` sorting
+        # ranks by match distance so the closest match lands on top (the
+        # per-keystroke modules — calc/emoji — opt out per-invocation with
+        # -no-sort).
+        #
+        # NOT `fzf`: rofi 2.0.0's fzf sorter mis-ranks with fuzzy matching —
+        # typing "steam" left ghostty selected on top instead of Steam
+        # (confirmed on hardware: `-sorting-method normal` and `-matching
+        # normal` both fixed it, `-no-sort` did not). Keep fuzzy matching for
+        # forgiveness; use the normal sorter to rank it (item 31).
         matching = "fuzzy";
         case-sensitive = false;
         sort = true;
-        sorting-method = "fzf";
+        sorting-method = "normal";
       };
 
       # Whole-swap themes bring their own rofi.rasi; otherwise the theme