diff --git a/docs/conversation-view.md b/docs/conversation-view.md
index 398c5c5..a877415 100644
--- a/docs/conversation-view.md
+++ b/docs/conversation-view.md
@@ -256,7 +256,17 @@ pane with nothing to render (a shell) simply stays a terminal.
 - **The prompt band spans the pane.** Reaching into the left gutter but stopping at the text
   column on the right made it read as a card floating over the answer rather than as the head of
   it. Full bleed both sides; the meta row sits tight under the band it belongs to, and one
-  exchange ends well before the next begins.
+  exchange ends well before the next begins. The bleed is `var(--cx-gutter)`, the same variable
+  `.cxv-body` pays out as padding, because the phone breakpoint narrows that padding: a bleed
+  that restated the desktop number stayed 14px against 8px of gutter and made the conversation
+  column scroll sideways on a phone.
+- **Nothing in the conversation scrolls sideways except the things meant to.** A code block and a
+  wide table each scroll inside their own box (`overflow-x: auto` on `pre` and `table`); the page,
+  the reading column and the answer do not. Prose therefore has to *wrap*, including a long URL
+  or an unbroken identifier — one long word is enough to push a paragraph wider than a phone, and
+  `.markdown` turns that into a sideways drag because a scroller in one axis makes the other axis
+  a scroller too. `overflow-x: hidden` on a parent is not the fix: it hides the symptom and clips
+  content people need to read.
 - **The reader fills the pane.** A fixed reading column left a gutter of nothing on each
   side while the prompt band still spanned the full width, so the two disagreed about where the
   conversation began. The pane is the measure: narrow the pane and the conversation narrows.
diff --git a/web/src/conversation.css b/web/src/conversation.css
index 3d21b51..3e67d0a 100644
--- a/web/src/conversation.css
+++ b/web/src/conversation.css
@@ -192,7 +192,11 @@ mark.cx-hit.on { background: var(--accent); color: var(--panel); }
    you scan for — still spanned the full width, so the two disagreed about where
    the conversation began. The pane is the measure: make it narrow and the
    conversation is narrow. */
-.cxv-body { flex: 1; min-height: 0; overflow-y: auto; overscroll-behavior: contain; background: var(--panel); padding: 4px 14px 30px; }
+/* The gutter is a variable because the prompt band bleeds INTO it (below). A
+   hardcoded bleed against a padding that changes at a breakpoint drifts apart,
+   and the band ends up wider than the scroller it sits in — which is exactly
+   how the phone gained a sideways scroll: 14px of bleed, 8px of padding. */
+.cxv-body { --cx-gutter: 14px; flex: 1; min-height: 0; overflow-y: auto; overscroll-behavior: contain; background: var(--panel); padding: 4px var(--cx-gutter) 30px; }
 .cxv-col { display: flex; flex-direction: column; min-width: 0; }
 .cxv-msg { font-size: 0.85em; color: var(--muted); padding: 6px 0; }
 /* The line above the oldest loaded exchange. Fixed height on purpose: it sits
@@ -231,7 +235,7 @@ mark.cx-hit.on { background: var(--accent); color: var(--panel); }
    text column on the right made it read as a card floating over the answer
    rather than as the head of it. Full bleed both sides, with the text inside
    still on the column. */
-.cxv-col .cx-prompt { margin-right: -14px; padding-right: 14px; }
+.cxv-col .cx-prompt { margin-right: calc(-1 * var(--cx-gutter)); padding-right: var(--cx-gutter); }
 .cxv-body > .cxv-col > .cx { padding-left: 16px; }
 
 /* Grouping: the meta row is the prompt's, not the answer's, so it sits tight
@@ -241,7 +245,7 @@ mark.cx-hit.on { background: var(--accent); color: var(--panel); }
 
 /* ---------- phone ---------- */
 @media (max-width: 720px) {
-  .cxv-body { padding: 4px 8px 24px; }
+  .cxv-body { --cx-gutter: 8px; padding: 4px var(--cx-gutter) 24px; }
   .cs-detail { font-size: 1em; }
 }
 
diff --git a/web/src/styles.css b/web/src/styles.css
index d6d83b6..ee57984 100644
--- a/web/src/styles.css
+++ b/web/src/styles.css
@@ -1147,6 +1147,17 @@ a.btn-ghost { text-decoration: none; }
 .markdown th, .markdown td { border: 1px solid var(--border); padding: 6px 10px; }
 .markdown img { max-width: 100%; }
 .markdown hr { border: none; border-top: 1px solid var(--border); margin: 16px 0; }
+/* Prose wraps; only genuinely wide content scrolls. A URL or an unbroken
+   identifier is one long word, and a long word made the paragraph wider than
+   the pane — which .markdown then scrolled sideways, because a scroller in one
+   axis makes the other axis a scroller too (overflow-y: auto above). Reported
+   on a phone, where the pane is narrow enough for ordinary prose to do it.
+   `pre` and `table` keep their own overflow-x: auto: a code block or a wide
+   table is meant to scroll, inside its own box, and breaking a line of code to
+   fit would change what it says. */
+.markdown p, .markdown li, .markdown blockquote,
+.markdown h1, .markdown h2, .markdown h3, .markdown h4 { overflow-wrap: anywhere; }
+.markdown :not(pre) > code { overflow-wrap: anywhere; }
 
 /* usage page */
 .usage { display: flex; flex-direction: column; gap: 12px; margin-top: 12px; }